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Moreover, the (𝐶, α)-means of a function 𝑓 ∈ 𝐿1 converge a.e. to 𝑓 as 𝑛 → ∞." /> <meta property="article:author" content="https://unideb.academia.edu/GyorgyGat" /> <meta name="description" content="We prove that the maximal operator of the (𝐶, α)-means of quadratical partial sums of double Vilenkin–Fourier series is of weak type (1,1). Moreover, the (𝐶, α)-means of a function 𝑓 ∈ 𝐿1 converge a.e. to 𝑓 as 𝑛 → ∞." /> <title>(PDF) Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series | Gyorgy Gat - Academia.edu</title> <link rel="canonical" href="https://www.academia.edu/68924112/Almost_Everywhere_Convergence_of_C_%CE%B1_Means_of_Quadratical_Partial_Sums_of_Double_Vilenkin_Fourier_Series" /> <script async src="https://www.googletagmanager.com/gtag/js?id=G-5VKX33P2DS"></script> <script> window.dataLayer = window.dataLayer || []; function gtag(){dataLayer.push(arguments);} gtag('js', new Date()); gtag('config', 'G-5VKX33P2DS', { cookie_domain: 'academia.edu', send_page_view: false, }); gtag('event', 'page_view', { 'controller': "single_work", 'action': "show", 'controller_action': 'single_work#show', 'logged_in': 'false', 'edge': 'unknown', // Send nil if there is no A/B test bucket, in case some records get logged // with missing data - that way we can distinguish between the two cases. // ab_test_bucket should be of the form <ab_test_name>:<bucket> 'ab_test_bucket': null, }) </script> <script> var $controller_name = 'single_work'; var $action_name = "show"; var $rails_env = 'production'; var $app_rev = '48654d67e5106e06fb1e5c9a356c302510d6cfee'; var $domain = 'academia.edu'; var $app_host = "academia.edu"; var $asset_host = "academia-assets.com"; var $start_time = new Date().getTime(); var $recaptcha_key = "6LdxlRMTAAAAADnu_zyLhLg0YF9uACwz78shpjJB"; var $recaptcha_invisible_key = "6Lf3KHUUAAAAACggoMpmGJdQDtiyrjVlvGJ6BbAj"; var $disableClientRecordHit = false; </script> <script> window.require = { config: function() { return function() {} } } </script> <script> window.Aedu = window.Aedu || {}; window.Aedu.hit_data = null; window.Aedu.serverRenderTime = new Date(1734498624000); window.Aedu.timeDifference = new Date().getTime() - 1734498624000; </script> <script type="application/ld+json">{"@context":"https://schema.org","@type":"ScholarlyArticle","abstract":"We prove that the maximal operator of the (𝐶, α)-means of quadratical partial sums of double Vilenkin–Fourier series is of weak type (1,1). 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Moreover, the (𝐶, α)-means of a function 𝑓 ∈ 𝐿1 converge a.e. to 𝑓 as 𝑛 → ∞.","publisher":"Walter de Gruyter GmbH","publication_name":"gmj"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–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 = "control"; 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":79223058,"attachmentType":"pdf"}"><img alt="First page of “Almost Everywhere Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–Fourier Series”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/79223058/mini_magick20220120-5931-11chag7.png?1642745578" /><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 Convergence of (𝐶, α)-Means of Quadratical Partial Sums of Double Vilenkin–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">gmj</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">16 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 = 68924112; 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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">We prove that the maximal operator of the (𝐶, α)-means of quadratical partial sums of double Vilenkin–Fourier series is of weak type (1,1). Moreover, the (𝐶, α)-means of a function 𝑓 ∈ 𝐿1 converge a.e. to 𝑓 as 𝑛 → ∞.</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":79223058,"attachmentType":"pdf","workUrl":"https://www.academia.edu/68924112/Almost_Everywhere_Convergence_of_C_%CE%B1_Means_of_Quadratical_Partial_Sums_of_Double_Vilenkin_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":79223058,"attachmentType":"pdf","workUrl":"https://www.academia.edu/68924112/Almost_Everywhere_Convergence_of_C_%CE%B1_Means_of_Quadratical_Partial_Sums_of_Double_Vilenkin_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="79223058" data-landing_url="https://www.academia.edu/68924112/Almost_Everywhere_Convergence_of_C_%CE%B1_Means_of_Quadratical_Partial_Sums_of_Double_Vilenkin_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="68924079" 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/68924079/Almost_Everywhere_Convergence_of_left_C_alpha_right_Means_of_Quadratical_Partial_sums_of_double_Vilenkin_Fourier_Series">Almost Everywhere Convergence of $\left( C,\alpha \right) $ -Means of Quadratical Partial sums of double Vilenkin-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">Georgian Mathematical Journal</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we prove that the maximal operator of the $\left( C,\alpha \right) $-means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1,1). 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SERIES","attachmentId":86520973,"attachmentType":"pdf","work_url":"https://www.academia.edu/79990907/Journal_of_Inequalities_in_Pure_and_Applied_Mathematics_MAXIMAL_OPERATORS_OF_FEJ%C3%89R_MEANS_OF_VILENKIN_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/79990907/Journal_of_Inequalities_in_Pure_and_Applied_Mathematics_MAXIMAL_OPERATORS_OF_FEJ%C3%89R_MEANS_OF_VILENKIN_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="68924076" 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/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-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">Georgian Mathematical Journal</p><p class="ds-related-work--abstract ds2-5-body-sm">The main aim of this paper is to prove that the (C,α)-means of quadratic partial sums of double Walsh-Kaczmarz-Fourier series are of weak type (1, 1) and of type (p,p) for all 1&lt;p≤∞(0&lt;α&lt;1). Moreover, these (C,α)-means converge to f almost everywhere for any integrable 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":"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-wsj-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-wsj-grid-card" data-collection-position="6" data-entity-id="86920320" 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/86920320/A_weak_type_inequality_for_the_maximal_operator_of_C_%CE%B1_means_of_Fourier_series_with_respect_to_the_Walsh_Kaczmarz_system">A weak type inequality for the maximal operator of (C, α)-means of Fourier series with respect to the Walsh-Kaczmarz 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">Acta Mathematica Hungarica, 2009</p><p class="ds-related-work--abstract ds2-5-body-sm">Simon [12] proved that the maximal operator of (C, α)-means of Fourier series with respect to the WalshKaczmarz system is bounded from the martingale Hardy space H p to the space Lp for p > 1/(1 + α). In this paper we prove that this boundedness result does not hold if p 1/(1 + α). However, in the endpoint case p = 1/(1 + α) the maximal operator σ α,k * is bounded from the martingale Hardy space H 1/(1+α) to the space weak-L 1/(1+α) .</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 weak type inequality for the maximal operator of (C, α)-means of Fourier series with respect to the Walsh-Kaczmarz system","attachmentId":91267311,"attachmentType":"pdf","work_url":"https://www.academia.edu/86920320/A_weak_type_inequality_for_the_maximal_operator_of_C_%CE%B1_means_of_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-wsj-grid-card-view-pdf" href="https://www.academia.edu/86920320/A_weak_type_inequality_for_the_maximal_operator_of_C_%CE%B1_means_of_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-wsj-grid-card" data-collection-position="7" data-entity-id="86377210" 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/86377210/A_note_on_The_maximal_operators_of_the_N_orlund_logaritmic_means_of_Vilenkin_Fourier_series">A note on The maximal operators of the N\"orlund logaritmic means of Vilenkin-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="127157369" href="https://independent.academia.edu/Tutberidze">Giorgi Tutberidze</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2019</p><p class="ds-related-work--abstract ds2-5-body-sm">The main aim of this paper is to investigate $\left(H_{p},L_{p}\right)$- type inequalities for the the maximal operators of N\&quot;orlund logaritmic means, for $0</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 note on The maximal operators of the N\\\"orlund logaritmic means of Vilenkin-Fourier series","attachmentId":90843392,"attachmentType":"pdf","work_url":"https://www.academia.edu/86377210/A_note_on_The_maximal_operators_of_the_N_orlund_logaritmic_means_of_Vilenkin_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/86377210/A_note_on_The_maximal_operators_of_the_N_orlund_logaritmic_means_of_Vilenkin_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="8" data-entity-id="19602101" 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/19602101/Mean_and_Almost_Everywhere_Convergence_of_Fourier_Neumann_Series">Mean and Almost Everywhere Convergence of Fourier–Neumann 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="39412258" href="https://independent.academia.edu/joseGuadalupe19">jose Guadalupe</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Mathematical Analysis and Applications, 1999</p><p class="ds-related-work--abstract ds2-5-body-sm">Let Jµ denote the Bessel function of order µ. The functions x −α/2−β/2−1/2 J α+β+2n+1 (x 1/2 ), n = 0, 1, 2, . . . , form an orthogonal system in L 2 ((0, ∞), x α+β dx) when α + β > −1. In this paper we analyze the range of p, α and β for which the Fourier series with respect to this system converges in the L p ((0, ∞), x α dx)-norm. Also, we describe the space in which the span of the system is dense and we show some of its properties. Finally, we study the almost everywhere convergence of the Fourier series for functions in such spaces.</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":"Mean and Almost Everywhere Convergence of Fourier–Neumann Series","attachmentId":42073418,"attachmentType":"pdf","work_url":"https://www.academia.edu/19602101/Mean_and_Almost_Everywhere_Convergence_of_Fourier_Neumann_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/19602101/Mean_and_Almost_Everywhere_Convergence_of_Fourier_Neumann_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="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></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":79223058,"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":79223058,"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_79223058" 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. 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data-collection-position="12" data-entity-id="110444318" 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/110444318/Norm_Convergence_of_Double_Fej%C3%A9r_Means_on_Unbounded_Vilenkin_Groups">Norm Convergence of Double Fejér Means on Unbounded Vilenkin Groups</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 Mathematica, 2018</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":"Norm Convergence of Double Fejér Means on Unbounded Vilenkin 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href="https://www.academia.edu/86377258/a_e_Convergence_of_N%C3%B6rlund_means_with_respect_to_Vilenkin_systems_of_integrable_functions">a.e. 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