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Namely, we prove the a.e. relation (1 n n−1 m=0 |Smmf − f | p) 1/p → 0 for every two-dimensional functions belonging to L" /> <meta name="twitter:image" content="https://0.academia-photos.com/32476274/18444977/18396189/s200_gyorgy.gat.jpg" /> <meta property="fb:app_id" content="2369844204" /> <meta property="og:type" content="article" /> <meta property="og:url" content="https://www.academia.edu/68924074/Almost_everywhere_strong_summability_of_Marcinkiewicz_means_of_double_Walsh_Fourier_series" /> <meta property="og:title" content="Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series" /> <meta property="og:image" content="http://a.academia-assets.com/images/open-graph-icons/fb-paper.gif" /> <meta property="og:description" content="In this paper we study the a. e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. 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"https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F68924074%2FAlmost_everywhere_strong_summability_of_Marcinkiewicz_means_of_double_Walsh_Fourier_series%3Fauto%3Ddownload"; window.loswp.translateUrl = "https://www.academia.edu/login?post_login_redirect_url=https%3A%2F%2Fwww.academia.edu%2F68924074%2FAlmost_everywhere_strong_summability_of_Marcinkiewicz_means_of_double_Walsh_Fourier_series%3Fshow_translation%3Dtrue"; window.loswp.previewableAttachments = [{"id":79223376,"identifier":"Attachment_79223376","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":68924074,"created_at":"2022-01-20T22:06:04.097-08:00","from_world_paper_id":192735806,"updated_at":"2024-11-25T03:18:28.023-08:00","_data":{"publisher":"Springer Nature","grobid_abstract":"In this paper we study the a. e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. Namely, we prove the a.e. relation (1 n n−1 m=0 |Smmf − f | p) 1/p → 0 for every two-dimensional functions belonging to L log L and 0 \u003c p ≤ 2. From the theorem of Getsadze [6] it follows that the space L log L can not be enlarged with preserving this strong summability property.","publication_date":"2014,,","publication_name":"Analysis Mathematica","grobid_abstract_attachment_id":"79223376"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series","broadcastable":false,"draft":null,"has_indexable_attachment":true,"indexable":true}}["work"]; window.loswp.workCoauthors = [32476274]; window.loswp.locale = "en"; window.loswp.countryCode = "SG"; window.loswp.cwvAbTestBucket = ""; window.loswp.designVariant = "ds_vanilla"; window.loswp.fullPageMobileSutdModalVariant = "full_page_mobile_sutd_modal"; window.loswp.useOptimizedScribd4genScript = false; window.loginModal = {}; window.loginModal.appleClientId = 'edu.academia.applesignon';</script><script defer="" src="https://accounts.google.com/gsi/client"></script><div class="ds-loswp-container"><div class="ds-work-card--grid-container"><div class="ds-work-card--container js-loswp-work-card"><div class="ds-work-card--cover"><div class="ds-work-cover--wrapper"><div class="ds-work-cover--container"><button class="ds-work-cover--clickable js-swp-download-button" data-signup-modal="{"location":"swp-splash-paper-cover","attachmentId":79223376,"attachmentType":"pdf"}"><img alt="First page of “Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/79223376/mini_magick20220120-19692-9axd3n.png?1642745762" /><img alt="PDF Icon" class="ds-work-cover--file-icon" src="//a.academia-assets.com/images/single_work_splash/adobe_icon.svg" /><div class="ds-work-cover--hover-container"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span><p>Download Free PDF</p></div><div class="ds-work-cover--ribbon-container">Download Free PDF</div><div class="ds-work-cover--ribbon-triangle"></div></button></div></div></div><div class="ds-work-card--work-information"><h1 class="ds-work-card--work-title">Almost everywhere strong summability of Marcinkiewicz means of double Walsh-Fourier series</h1><div class="ds-work-card--work-authors ds-work-card--detail"><a class="ds-work-card--author js-wsj-grid-card-author ds2-5-body-md ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat"><img alt="Profile image of Gyorgy Gat" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/32476274/18444977/18396189/s65_gyorgy.gat.jpg" />Gyorgy Gat</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2014, Analysis Mathematica</p><div class="ds-work-card--work-metadata"><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">visibility</span><p class="ds2-5-body-sm" id="work-metadata-view-count">…</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">description</span><p class="ds2-5-body-sm">19 pages</p></div><div class="ds-work-card--work-metadata__stat"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">link</span><p class="ds2-5-body-sm">1 file</p></div></div><script>(async () => { const workId = 68924074; 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if (!viewCountBody) { throw new Error('Failed to find work views element'); } viewCountBody.textContent = `${commaizedViewCount} views`; } catch (error) { // Remove the whole views element if there was some issue parsing. document.getElementById('work-metadata-view-count')?.parentNode?.remove(); throw new Error(`Failed to parse view count: ${viewCount}`, error); } }; // If the DOM is still loading, wait for it to be ready before updating the view count. if (document.readyState === "loading") { document.addEventListener('DOMContentLoaded', () => { updateViewCount(viewCount); }); // Otherwise, just update it immediately. } else { updateViewCount(viewCount); } })();</script></div><p class="ds-work-card--work-abstract ds-work-card--detail ds2-5-body-md">In this paper we study the a. e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. Namely, we prove the a.e. relation (1 n n−1 m=0 |Smmf − f | p) 1/p → 0 for every two-dimensional functions belonging to L log L and 0 < p ≤ 2. From the theorem of Getsadze [6] it follows that the space L log L can not be enlarged with preserving this strong summability property.</p><div class="ds-work-card--button-container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--work-card","attachmentId":79223376,"attachmentType":"pdf","workUrl":"https://www.academia.edu/68924074/Almost_everywhere_strong_summability_of_Marcinkiewicz_means_of_double_Walsh_Fourier_series"}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--work-card","attachmentId":79223376,"attachmentType":"pdf","workUrl":"https://www.academia.edu/68924074/Almost_everywhere_strong_summability_of_Marcinkiewicz_means_of_double_Walsh_Fourier_series"}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div></div><div data-auto_select="false" data-client_id="331998490334-rsn3chp12mbkiqhl6e7lu2q0mlbu0f1b" data-doc_id="79223376" data-landing_url="https://www.academia.edu/68924074/Almost_everywhere_strong_summability_of_Marcinkiewicz_means_of_double_Walsh_Fourier_series" data-login_uri="https://www.academia.edu/registrations/google_one_tap" data-moment_callback="onGoogleOneTapEvent" id="g_id_onload"></div><div class="ds-top-related-works--grid-container"><div class="ds-related-content--container ds-top-related-works--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="0" data-entity-id="110444322" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/110444322/Almost_everywhere_strong_summability_of_double_Walsh_Fourier_series">Almost everywhere strong summability of double Walsh-Fourier series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Contemporary Mathematical Analysis, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we study the a. e. strong convergence of the quadratical partial sums of the two-dimensional Walsh-Fourier series. Namely, we prove the a.e. relation (1 n n−1 m=0 |Smmf − f | p) 1/p → 0 for every two-dimensional functions belonging to L log L and 0 < p ≤ 2. From the theorem of Getsadze [6] it follows that the space L log L can not be enlarged with preserving this strong summability property.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Almost everywhere strong summability of double Walsh-Fourier series","attachmentId":108260131,"attachmentType":"pdf","work_url":"https://www.academia.edu/110444322/Almost_everywhere_strong_summability_of_double_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/110444322/Almost_everywhere_strong_summability_of_double_Walsh_Fourier_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="1" data-entity-id="68924008" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924008/Convergence_in_measure_of_logarithmic_means_of_quadratical_partial_sums_of_double_Walsh_Fourier_series">Convergence in measure of logarithmic means of quadratical partial sums of double Walsh–Fourier series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2006</p><p class="ds-related-work--abstract ds2-5-body-sm">The main aim of this paper is to prove that the logarithmic means of the double Walsh-Fourier series do not improve the convergence in measure. In other words, we prove that for any Orlicz space, which is not a subspace of L log L(I 2), the set of functions for which quadratic logarithmic means of the double Walsh-Fourier series converge in measure is of first Baire category.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Convergence in measure of logarithmic means of quadratical partial sums of double Walsh–Fourier series","attachmentId":79223354,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924008/Convergence_in_measure_of_logarithmic_means_of_quadratical_partial_sums_of_double_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/68924008/Convergence_in_measure_of_logarithmic_means_of_quadratical_partial_sums_of_double_Walsh_Fourier_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="2" data-entity-id="65305605" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/65305605/Strong_Approximation_by_Marcinkiewicz_Means_of_Two_dimensional_Walsh_Fourier_Series">Strong Approximation by Marcinkiewicz Means of Two-dimensional Walsh-Fourier Series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="63716633" href="https://independent.academia.edu/LevanGogoladze">Levan Gogoladze</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Constructive Approximation, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we study the exponential uniform strong approximation of Marcinkiewicz type of two-dimensional Walsh-Kaczmarz-Fourier series. In particular, it is proved that the Marcinkiewicz type of two-dimensional Walsh-Kaczmarz-Fourier series of the continuous function f is uniformly strong summable to the function f exponentially in the power 1/2. Moreover, it is proved that this result is best possible.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Strong Approximation by Marcinkiewicz Means of Two-dimensional Walsh-Fourier Series","attachmentId":76962348,"attachmentType":"pdf","work_url":"https://www.academia.edu/65305605/Strong_Approximation_by_Marcinkiewicz_Means_of_Two_dimensional_Walsh_Fourier_Series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/65305605/Strong_Approximation_by_Marcinkiewicz_Means_of_Two_dimensional_Walsh_Fourier_Series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="3" data-entity-id="68924097" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924097/Almost_everywhere_convergence_of_a_subsequence_of_the_logarithmic_means_of_quadratical_partial_sums_of_double_Walsh_Fourier_series">Almost everywhere convergence of a subsequence of the logarithmic means of quadratical partial sums of double Walsh-Fourier series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Publicationes Mathematicae, 2007</p><p class="ds-related-work--abstract ds2-5-body-sm">The main aim of this paper is to prove that the maximal operator of the logarithmic means of quadratical partial sums of double Walsh-Fourier series is of weak type (1, 1) provided that the supremum in the maximal operator is taken over special indicies. The set of Walsh polynomials is dense in L 1 (I × I) , so by the well-known density argument we have that t 2 n f x 1 , x 2 → f x 1 , x 2 a. e. for all integrable two-variable function f .</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Almost everywhere convergence of a subsequence of the logarithmic means of quadratical partial sums of double Walsh-Fourier series","attachmentId":79223359,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924097/Almost_everywhere_convergence_of_a_subsequence_of_the_logarithmic_means_of_quadratical_partial_sums_of_double_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/68924097/Almost_everywhere_convergence_of_a_subsequence_of_the_logarithmic_means_of_quadratical_partial_sums_of_double_Walsh_Fourier_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="4" data-entity-id="68924085" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924085/A_remark_on_the_divergence_of_strong_power_means_of_Walsh_Fourier_series">A remark on the divergence of strong power means of Walsh-Fourier series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematical Notes, 2014</p><p class="ds-related-work--abstract ds2-5-body-sm">F. Schipp in 1969 proved almost everywhere p-strong summability of Walsh-Fourier series and if λ(n) → ∞ there exists a function f ∈ L 1 [0, 1) which Walsh partial sums S k (x, f) satisfy the divergence condition lim sup n→∞ 1 n n k=1 |S k (x, f)| λ(k) = ∞ almost everywhere on [0, 1). In the present paper we show that this condition may hold everywhere.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"A remark on the divergence of strong power means of Walsh-Fourier series","attachmentId":79223443,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924085/A_remark_on_the_divergence_of_strong_power_means_of_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/68924085/A_remark_on_the_divergence_of_strong_power_means_of_Walsh_Fourier_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="5" data-entity-id="110444351" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/110444351/Almost_Everywhere_Convergence_of_Fej%C3%A9r_Means_of_Two_dimensional_Triangular_Walsh_Fourier_Series">Almost Everywhere Convergence of Fejér Means of Two-dimensional Triangular Walsh–Fourier Series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Fourier Analysis and Applications, 2017</p><p class="ds-related-work--abstract ds2-5-body-sm">In 1987 Harris proved [11]-among others-that for each 1 ≤ p < 2 there exists a two-dimensional function f ∈ L p such that its triangular Walsh-Fourier series diverges almost everywhere. In this paper we investigate the Fejér (or (C, 1)) means of the triangle two variable Walsh-Fourier series of L 1 functions. Namely, we prove the a.e. convergence σ △ n f = 1 n n−1 k=0 S k,n−k f → f (n → ∞) for each integrable two-variable function f. 2010 Mathematics Subject Classification. 42C10.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Almost Everywhere Convergence of Fejér Means of Two-dimensional Triangular Walsh–Fourier Series","attachmentId":108260147,"attachmentType":"pdf","work_url":"https://www.academia.edu/110444351/Almost_Everywhere_Convergence_of_Fej%C3%A9r_Means_of_Two_dimensional_Triangular_Walsh_Fourier_Series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/110444351/Almost_Everywhere_Convergence_of_Fej%C3%A9r_Means_of_Two_dimensional_Triangular_Walsh_Fourier_Series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="6" data-entity-id="68924048" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924048/On_almost_everywhere_convergence_and_divergence_of_Marcinkiewicz_like_means_of_integrable_functions_with_respect_to_the_two_dimensional_Walsh_system">On almost everywhere convergence and divergence of Marcinkiewicz-like means of integrable functions with respect to the two-dimensional Walsh system</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Approximation Theory, 2012</p><p class="ds-related-work--abstract ds2-5-body-sm">Let |n| be the lower integer part of the binary logarithm of the positive integer n and α : N 2 → N 2. In this paper we generalize the notion of the two dimensional Marcinkiewicz means of Fourier series of two-variable integrable functions as t α n f := 1 n  n−1 k=0 S α(|n|,k) f and give a kind of necessary and sufficient condition for functions in order to have the almost everywhere relation t α n f → f for all f ∈ L 1 ([0, 1) 2) with respect to the Walsh-Paley system. The original version of the Marcinkiewicz means are defined by α(|n|, k) = (k, k) and discussed by a lot of authors. See for instance [13,</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On almost everywhere convergence and divergence of Marcinkiewicz-like means of integrable functions with respect to the two-dimensional Walsh system","attachmentId":79223064,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924048/On_almost_everywhere_convergence_and_divergence_of_Marcinkiewicz_like_means_of_integrable_functions_with_respect_to_the_two_dimensional_Walsh_system","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/68924048/On_almost_everywhere_convergence_and_divergence_of_Marcinkiewicz_like_means_of_integrable_functions_with_respect_to_the_two_dimensional_Walsh_system"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="7" data-entity-id="6119563" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/6119563/Strong_means_and_the_oscillation_of_multiple_Fourier_Walsh_series">Strong means and the oscillation of multiple Fourier-Walsh series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="9266195" href="https://bakustate.academia.edu/VladimirRodin">Vladimir Rodin</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Mathematical Notes, 1994</p><p class="ds-related-work--abstract ds2-5-body-sm">1. Using the method by Bochkarev, Kheladze proved [1] an analog of the Kolmogorov theorem on everywhere-divergent Fourier-Walsh-Paley series. Based on this result, it seems natural to use the apparatus of strong means to represent functions integrable on the group I-Ik Zk(2) = G.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Strong means and the oscillation of multiple Fourier-Walsh series","attachmentId":49010905,"attachmentType":"pdf","work_url":"https://www.academia.edu/6119563/Strong_means_and_the_oscillation_of_multiple_Fourier_Walsh_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/6119563/Strong_means_and_the_oscillation_of_multiple_Fourier_Walsh_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="8" data-entity-id="68924106" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924106/Maximal_Convergence_Space_of_a_Subsequence_of_the_Logarithmic_Means_of_Rectangular_Partial_Sums_of_Double_Walsh_Fourier_Series">Maximal Convergence Space of a Subsequence of the Logarithmic Means of Rectangular Partial Sums of Double Walsh-Fourier Series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Real Analysis Exchange</p><p class="ds-related-work--abstract ds2-5-body-sm">The main aim of this paper is to prove that the maximal operator of the logarithmic means of rectangular partial sums of double Walsh-Fourier series is of type (H # , L 1) provided that the supremum in the maximal operator is taken over some special indicies. The set of Walsh polynomials is dense in H # , so by the well-known density argument we have that t 2 n ,2 m f x 1 , x 2 → f x 1 , x 2 a. e. as m, n → ∞ for all f ∈ H # (⊃ L log + L). We also prove the sharpness of this result. Namely, For all measurable function δ : [0, +∞) → [0, +∞), lim t→∞ δ(t) = 0 we have a function f such as f ∈ Llog + Lδ(L) and the two-dimensional Nörlund logarithmic means does not converge to f a.e. (in the Pringsheim sense) on I 2 .</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Maximal Convergence Space of a Subsequence of the Logarithmic Means of Rectangular Partial Sums of Double Walsh-Fourier Series","attachmentId":79223372,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924106/Maximal_Convergence_Space_of_a_Subsequence_of_the_Logarithmic_Means_of_Rectangular_Partial_Sums_of_Double_Walsh_Fourier_Series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/68924106/Maximal_Convergence_Space_of_a_Subsequence_of_the_Logarithmic_Means_of_Rectangular_Partial_Sums_of_Double_Walsh_Fourier_Series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-wsj-grid-card" data-collection-position="9" data-entity-id="21953862" data-sort-order="default"><a class="ds-related-work--title js-wsj-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/21953862/Cesaro_Summability_of_Double_Walsh_Fourier_Series">Cesaro Summability of Double Walsh-Fourier Series</a><div class="ds-related-work--metadata"><a class="js-wsj-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="43203026" href="https://independent.academia.edu/FerencSchipp">Ferenc Schipp</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Transactions of the American Mathematical Society, 1992</p><p class="ds-related-work--abstract ds2-5-body-sm">We introduce Quasi-local operators (these include operators of Calderon-Zygmund type), a hybrid Hardy space H# of functions of two variables, and we obtain sufficient conditions for a Quasi-local maximal operator to be of weak type (", I). As an application, we show that Cesaro means of the double Walsh-Fourier series of a function f converge a.e. when f belongs to H#. We also obtain the dyadic analogue of a summability result of Marcienkiewicz and Zygmund valid for all fELl provided summability takes place in some positive cone.</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Cesaro Summability of Double Walsh-Fourier Series","attachmentId":42674062,"attachmentType":"pdf","work_url":"https://www.academia.edu/21953862/Cesaro_Summability_of_Double_Walsh_Fourier_Series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-wsj-grid-card-view-pdf" href="https://www.academia.edu/21953862/Cesaro_Summability_of_Double_Walsh_Fourier_Series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div></div></div><div class="ds-sticky-ctas--wrapper js-loswp-sticky-ctas hidden"><div class="ds-sticky-ctas--grid-container"><div class="ds-sticky-ctas--container"><button class="ds2-5-button js-swp-download-button" data-signup-modal="{"location":"continue-reading-button--sticky-ctas","attachmentId":79223376,"attachmentType":"pdf","workUrl":null}">See full PDF</button><button class="ds2-5-button ds2-5-button--secondary js-swp-download-button" data-signup-modal="{"location":"download-pdf-button--sticky-ctas","attachmentId":79223376,"attachmentType":"pdf","workUrl":null}"><span class="material-symbols-outlined" style="font-size: 20px" translate="no">download</span>Download PDF</button></div></div></div><div class="ds-below-fold--grid-container"><div class="ds-work--container js-loswp-embedded-document"><div class="attachment_preview" data-attachment="Attachment_79223376" style="display: none"><div class="js-scribd-document-container"><div class="scribd--document-loading js-scribd-document-loader" style="display: block;"><img alt="Loading..." src="//a.academia-assets.com/images/loaders/paper-load.gif" /><p>Loading Preview</p></div></div><div style="text-align: center;"><div class="scribd--no-preview-alert js-preview-unavailable"><p>Sorry, preview is currently unavailable. You can download the paper by clicking the button above.</p></div></div></div></div><div class="ds-sidebar--container js-work-sidebar"><div class="ds-related-content--container"><h2 class="ds-related-content--heading">Related papers</h2><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="0" data-entity-id="68924086" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924086/On_everywhere_divergence_of_the_strong_%CE%A6_means_of_Walsh_Fourier_series">On everywhere divergence of the strong Φ-means of Walsh–Fourier series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Mathematical Analysis and Applications, 2015</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On everywhere divergence of the strong Φ-means of Walsh–Fourier series","attachmentId":79223537,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924086/On_everywhere_divergence_of_the_strong_%CE%A6_means_of_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68924086/On_everywhere_divergence_of_the_strong_%CE%A6_means_of_Walsh_Fourier_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="1" data-entity-id="68924076" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924076/On_the_C_alpha_means_of_quadratic_partial_sums_of_double_Walsh_Kaczmarz_Fourier_series">On the $(C,\alpha)$-means of quadratic partial sums of double Walsh-Kaczmarz-Fourier series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Georgian Mathematical Journal</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the $(C,\\alpha)$-means of quadratic partial sums of double Walsh-Kaczmarz-Fourier series","attachmentId":79223212,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924076/On_the_C_alpha_means_of_quadratic_partial_sums_of_double_Walsh_Kaczmarz_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68924076/On_the_C_alpha_means_of_quadratic_partial_sums_of_double_Walsh_Kaczmarz_Fourier_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="2" data-entity-id="68923995" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68923995/On_the_divergence_of_the_C_1_means_of_double_Walsh_Fourier_series">On the divergence of the (C, 1) means of double Walsh-Fourier series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2000</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the divergence of the (C, 1) means of double Walsh-Fourier series","attachmentId":79223023,"attachmentType":"pdf","work_url":"https://www.academia.edu/68923995/On_the_divergence_of_the_C_1_means_of_double_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68923995/On_the_divergence_of_the_C_1_means_of_double_Walsh_Fourier_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="3" data-entity-id="68924006" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924006/On_the_Marcinkiewicz_Fej%C3%A9r_means_of_double_Fourier_series_with_respect_to_the_Walsh_Kaczmarz_system">On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"On the Marcinkiewicz-Fejér means of double Fourier series with respect to the Walsh-Kaczmarz system","attachmentId":79223203,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924006/On_the_Marcinkiewicz_Fej%C3%A9r_means_of_double_Fourier_series_with_respect_to_the_Walsh_Kaczmarz_system","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68924006/On_the_Marcinkiewicz_Fej%C3%A9r_means_of_double_Fourier_series_with_respect_to_the_Walsh_Kaczmarz_system"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="4" data-entity-id="110444339" data-sort-order="default"><a class="ds-related-work--title 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href="https://www.academia.edu/68924094/Uniform_and_L_convergence_of_logarithmic_means_of_cubical_partial_sums_of_double_Walsh_Fourier_series">Uniform and $L$-convergence of logarithmic means of cubical partial sums of double Walsh-Fourier series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2004</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Uniform and $L$-convergence of logarithmic means of cubical partial sums of double Walsh-Fourier 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href="https://www.academia.edu/68924061/Uniform_and_L_Convergence_of_Logarithmic_Means_of_Double_Walsh_Fourier_Series">Uniform and 𝐿-Convergence of Logarithmic Means of Double Walsh–Fourier Series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Uniform and 𝐿-Convergence of Logarithmic Means of Double Walsh–Fourier Series","attachmentId":79223039,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924061/Uniform_and_L_Convergence_of_Logarithmic_Means_of_Double_Walsh_Fourier_Series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68924061/Uniform_and_L_Convergence_of_Logarithmic_Means_of_Double_Walsh_Fourier_Series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="8" data-entity-id="68924007" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924007/Divergence_of_the_C_1_means_of_d_dimensional_Walsh_Fourier_series">Divergence of the (C, 1) means of d-dimensional Walsh-Fourier series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2001</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Divergence of the (C, 1) means of d-dimensional Walsh-Fourier series","attachmentId":79223200,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924007/Divergence_of_the_C_1_means_of_d_dimensional_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68924007/Divergence_of_the_C_1_means_of_d_dimensional_Walsh_Fourier_series"><span 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js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Uniform and L–convergence of Logarithmic Means of Walsh–Fourier Series","attachmentId":79223055,"attachmentType":"pdf","work_url":"https://www.academia.edu/68923982/Uniform_and_L_convergence_of_Logarithmic_Means_of_Walsh_Fourier_Series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68923982/Uniform_and_L_convergence_of_Logarithmic_Means_of_Walsh_Fourier_Series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="10" data-entity-id="68923986" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68923986/Convergence_of_logarithmic_means_of_multiple_Walsh_Fourier_series">Convergence of logarithmic means of multiple Walsh-Fourier series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Analysis in Theory and Applications, 2005</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Convergence of logarithmic means of multiple Walsh-Fourier 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href="https://www.academia.edu/14524342/Absolute_convergence_of_double_Walsh_Fourier_series_and_related_results">Absolute convergence of double Walsh–Fourier series and related results</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33480643" href="https://independent.academia.edu/FerencM%C3%B3ricz">Ferenc Móricz</a><span>, </span><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="33525817" href="https://independent.academia.edu/AntalVeres">Antal Veres</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Acta Mathematica Hungarica, 2011</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Absolute convergence of double Walsh–Fourier series and related 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href="https://www.academia.edu/5316802/Lacunary_Fourier_and_Walsh_Fourier_series_near_L_1">Lacunary Fourier and Walsh-Fourier series near L^1</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="2000086" href="https://brown.academia.edu/FrancescoDiPlinio">Francesco Di Plinio</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2013</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Lacunary Fourier and Walsh-Fourier series near L^1","attachmentId":32479273,"attachmentType":"pdf","work_url":"https://www.academia.edu/5316802/Lacunary_Fourier_and_Walsh_Fourier_series_near_L_1","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/5316802/Lacunary_Fourier_and_Walsh_Fourier_series_near_L_1"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="13" data-entity-id="68924066" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68924066/Summation_of_Walsh_Fourier_Series_Convergence_and_Divergence">Summation of Walsh-Fourier Series, Convergence and Divergence</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Summation of Walsh-Fourier Series, Convergence and Divergence","attachmentId":79223038,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924066/Summation_of_Walsh_Fourier_Series_Convergence_and_Divergence","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68924066/Summation_of_Walsh_Fourier_Series_Convergence_and_Divergence"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="14" data-entity-id="68923996" data-sort-order="default"><a class="ds-related-work--title js-related-work-grid-card-title ds2-5-body-md ds2-5-body-link" href="https://www.academia.edu/68923996/Pointwise_convergence_of_the_Cesaro_means_of_double_Walsh_series">Pointwise convergence of the Cesaro means of double Walsh series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">1996</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Pointwise convergence of the Cesaro means of double Walsh 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href="https://www.academia.edu/68923984/Pointwise_convergence_of_cone_like_restricted_two_dimensional_Fej%C3%A9r_means_of_Walsh_Fourier_series">Pointwise convergence of cone-like restricted two-dimensional Fejér means of Walsh-Fourier series</a><div class="ds-related-work--metadata"><a class="js-related-work-grid-card-author ds2-5-body-sm ds2-5-body-link" data-author-id="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Acta Mathematica Sinica, English Series, 2010</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" data-signup-modal="{"location":"wsj-grid-card-download-pdf-modal","work_title":"Pointwise convergence of cone-like restricted two-dimensional Fejér means of Walsh-Fourier series","attachmentId":79223364,"attachmentType":"pdf","work_url":"https://www.academia.edu/68923984/Pointwise_convergence_of_cone_like_restricted_two_dimensional_Fej%C3%A9r_means_of_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" href="https://www.academia.edu/68923984/Pointwise_convergence_of_cone_like_restricted_two_dimensional_Fej%C3%A9r_means_of_Walsh_Fourier_series"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" translate="no">chevron_right</span></a></div></div><div class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="16" data-entity-id="79991379" data-sort-order="default"><a class="ds-related-work--title 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