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window.loswp.work = {"work":{"id":86377209,"created_at":"2022-09-09T15:11:18.943-07:00","from_world_paper_id":214664481,"updated_at":"2024-06-11T00:15:07.922-07:00","_data":{"abstract":"In this paper we derive a new strong convergence theorem of Riesz logarithmic means of the one-dimensional Vilenkin–Fourier (Walsh–Fourier) series. The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh–Fourier series.","publisher":"Springer Science and Business Media LLC","publication_date":"2020,,","publication_name":"Journal of Inequalities and Applications"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Some inequalities related to strong convergence of Riesz logarithmic means","broadcastable":true,"draft":null,"has_indexable_attachment":true,"indexable":true,"seo_quality":null}}["work"]; window.loswp.workCoauthors = [127157369]; 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'; window.userInChina = "false";</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":90843386,"attachmentType":"pdf"}"><img alt="First page of “Some inequalities related to strong convergence of Riesz logarithmic means”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/90843386/mini_magick20220909-1-9hd9k0.png?1662761646" /><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">Some inequalities related to strong convergence of Riesz logarithmic means</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="127157369" href="https://independent.academia.edu/Tutberidze"><img alt="Profile image of Giorgi Tutberidze" class="ds-work-card--author-avatar" src="https://0.academia-photos.com/127157369/37666740/31788622/s65_giorgi.tutberidze.jpg" />Giorgi Tutberidze</a></div><div class="ds-work-card--detail"><p class="ds-work-card--detail ds2-5-body-sm">2020, Journal of Inequalities and Applications</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">17 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 = 86377209; 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The corresponding inequality is pointed out and it is also proved that the inequality is in a sense sharp, at least for the case with Walsh–Fourier series.</p></div></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="68923986" 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/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-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">Analysis in Theory and Applications, 2005</p><p class="ds-related-work--abstract ds2-5-body-sm">Nörlund logarithmic means of multiple Walsh-Fourier series acting from spaceLlnd-1 L([0, 1)d), d&gt;-1 into space weak-L1([0, 1)d) are studied. The maximal Orlicz space such that the Nörlund logarithmic means of multiple Walsh-Fourier series for the functions from this space converge in d-dimensional measure is found.</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 series","attachmentId":79222978,"attachmentType":"pdf","work_url":"https://www.academia.edu/68923986/Convergence_of_logarithmic_means_of_multiple_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/68923986/Convergence_of_logarithmic_means_of_multiple_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="68924055" 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/68924055/Convergence_in_measure_of_logarithmic_means_of_multiple_Fourier_series">Convergence in measure of logarithmic means of multiple 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, 2014</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 multiple Fourier series","attachmentId":79223357,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924055/Convergence_in_measure_of_logarithmic_means_of_multiple_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/68924055/Convergence_in_measure_of_logarithmic_means_of_multiple_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="110444357" 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/110444357/Almost_everywhere_convergence_of_a_subsequence_of_the_logarithmic_means_of_Vilenkin_Fourier_series">Almost everywhere convergence of a subsequence of the logarithmic 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="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Facta universitatis. Series electronics and energetics, 2008</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 a subsequence of the (one-dimensional) logarithmic means of Vilenkin-Fourier series is of weak type (1, 1). Moreover, we prove that the maximal operator of the logarithmic means of quadratical partial sums of double Vilenkin-Fourier series is of weak type (1, 1), provided that the supremum in the maximal operator is taken over special indices. The set of Vilenkin polynomials is dense in L 1 , so by the well-known density argument the logarithmic means t 2 n (f) converge a.e. to f for all 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":"Almost everywhere convergence of a subsequence of the logarithmic means of Vilenkin-Fourier series","attachmentId":108260151,"attachmentType":"pdf","work_url":"https://www.academia.edu/110444357/Almost_everywhere_convergence_of_a_subsequence_of_the_logarithmic_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/110444357/Almost_everywhere_convergence_of_a_subsequence_of_the_logarithmic_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="4" data-entity-id="68923982" 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/68923982/Uniform_and_L_convergence_of_Logarithmic_Means_of_Walsh_Fourier_Series">Uniform and L–convergence of Logarithmic 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">Acta Mathematica Sinica, English Series, 2006</p><p class="ds-related-work--abstract ds2-5-body-sm">We discuss some convergence and divergence properties of twodimensional (Nörlund) logarithmic means of two-dimensional Walsh-Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.</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 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-wsj-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-wsj-grid-card" data-collection-position="5" 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="6" data-entity-id="68924061" 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/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-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--abstract ds2-5-body-sm">We discuss some convergence and divergence properties of twodimensional (Nörlund) logarithmic means of two-dimensional Walsh-Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.</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 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-wsj-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-wsj-grid-card" data-collection-position="7" data-entity-id="68924074" 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/68924074/Almost_everywhere_strong_summability_of_Marcinkiewicz_means_of_double_Walsh_Fourier_series">Almost everywhere strong summability of Marcinkiewicz means 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">Analysis Mathematica, 2014</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 Marcinkiewicz means of double Walsh-Fourier series","attachmentId":79223376,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924074/Almost_everywhere_strong_summability_of_Marcinkiewicz_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-wsj-grid-card-view-pdf" href="https://www.academia.edu/68924074/Almost_everywhere_strong_summability_of_Marcinkiewicz_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-wsj-grid-card" data-collection-position="8" data-entity-id="68924086" 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/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-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 Mathematical Analysis and Applications, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">Almost everywhere strong exponential summability of Fourier series in Walsh and trigonometric systems established by Rodin in 1990. We prove, that if the growth of a function Φ(t) : [0, ∞) → [0, ∞) is bigger than the exponent, then the strong Φ-summability of a Walsh-Fourier series can fail everywhere. The analogous theorem for trigonometric system was proved before by one of the author of this paper.</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-wsj-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-wsj-grid-card" data-collection-position="9" data-entity-id="68924094" 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/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-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">2004</p><p class="ds-related-work--abstract ds2-5-body-sm">We discuss some convergence and divergence properties of twodimensional (Nörlund) logarithmic means of two-dimensional Walsh-Fourier series of functions both in the uniform and in the Lebesgue norm. We give necessary and sufficient conditions for the convergence regarding the modulus of continuity of the function, and also the function space.</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 series","attachmentId":79223452,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924094/Uniform_and_L_convergence_of_logarithmic_means_of_cubical_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/68924094/Uniform_and_L_convergence_of_logarithmic_means_of_cubical_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":90843386,"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":90843386,"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_90843386" 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="68924097" 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/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-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">Publicationes Mathematicae, 2007</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-related-work-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-related-work-sidebar-card" data-collection-position="1" data-entity-id="121005737" 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/121005737/Some_inequalities_for_Ces%C3%A0ro_means_of_double_Vilenkin_Fourier_series">Some inequalities for Cesàro means of double Vilenkin–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="311378547" href="https://independent.academia.edu/PerssonLarsErik">Lars-Erik Persson</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Journal of Inequalities and Applications, 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":"Some inequalities for Cesàro means of double Vilenkin–Fourier series","attachmentId":115986554,"attachmentType":"pdf","work_url":"https://www.academia.edu/121005737/Some_inequalities_for_Ces%C3%A0ro_means_of_double_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-related-work-grid-card-view-pdf" href="https://www.academia.edu/121005737/Some_inequalities_for_Ces%C3%A0ro_means_of_double_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-related-work-sidebar-card" data-collection-position="2" data-entity-id="68923983" 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/68923983/On_the_divergence_of_N%C3%B6rlund_logarithmic_means_of_Walsh_Fourier_series">On the divergence of Nörlund logarithmic 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, 2009</p><div class="ds-related-work--ctas"><button class="ds2-5-text-link ds2-5-text-link--inline js-swp-download-button" 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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-related-work-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><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 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Mathematicae Debrecen, 2014</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 convergence theorem for Vilenkin--Fejer means","attachmentId":86521217,"attachmentType":"pdf","work_url":"https://www.academia.edu/79991268/Strong_convergence_theorem_for_Vilenkin_Fejer_means","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/79991268/Strong_convergence_theorem_for_Vilenkin_Fejer_means"><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 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Blahota</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Tohoku Mathematical Journal, 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":"Strong convergence theorem of Cesàro means with respect to the Walsh system","attachmentId":86521281,"attachmentType":"pdf","work_url":"https://www.academia.edu/79991379/Strong_convergence_theorem_of_Ces%C3%A0ro_means_with_respect_to_the_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-related-work-grid-card-view-pdf" href="https://www.academia.edu/79991379/Strong_convergence_theorem_of_Ces%C3%A0ro_means_with_respect_to_the_Walsh_system"><span class="ds2-5-text-link__content">View 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