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This convergence theorem of Hardy-Littlewood type for the ordinary Vilenkin system was proved in 1954 by Yano.","publication_date":"1998,,","grobid_abstract_attachment_id":"79223356"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"On a theorem of type Hardy–Littlewood with respect to the Vilenkin-like systems","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":79223356,"attachmentType":"pdf"}"><img alt="First page of “On a theorem of type Hardy–Littlewood with respect to the Vilenkin-like systems”" class="ds-work-cover--cover-thumbnail" src="https://0.academia-photos.com/attachment_thumbnails/79223356/mini_magick20220120-5937-19y8nz0.png?1642745662" /><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">On a theorem of type Hardy–Littlewood with respect to the Vilenkin-like systems</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">1998</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">6 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 = 68924044; 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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 give a convergence test for generalized (by the author) Vilenkin-Fourier series. This convergence theorem of Hardy-Littlewood type for the ordinary Vilenkin system was proved in 1954 by Yano.</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":79223356,"attachmentType":"pdf","workUrl":"https://www.academia.edu/68924044/On_a_theorem_of_type_Hardy_Littlewood_with_respect_to_the_Vilenkin_like_systems"}">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":79223356,"attachmentType":"pdf","workUrl":"https://www.academia.edu/68924044/On_a_theorem_of_type_Hardy_Littlewood_with_respect_to_the_Vilenkin_like_systems"}"><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="79223356" data-landing_url="https://www.academia.edu/68924044/On_a_theorem_of_type_Hardy_Littlewood_with_respect_to_the_Vilenkin_like_systems" 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="86377257" 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/86377257/On_the_strong_convergence_of_partial_sums_with_respect_to_bounded_Vilenkin_systems">On the strong convergence of partial sums with respect to bounded Vilenkin systems</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">arXiv: Classical Analysis and ODEs, 2018</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we investigate some strong convergence theorems for partial sums with respect to Vilenkin system.</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 strong convergence of partial sums with respect to bounded Vilenkin systems","attachmentId":90843462,"attachmentType":"pdf","work_url":"https://www.academia.edu/86377257/On_the_strong_convergence_of_partial_sums_with_respect_to_bounded_Vilenkin_systems","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/86377257/On_the_strong_convergence_of_partial_sums_with_respect_to_bounded_Vilenkin_systems"><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="85415280" 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/85415280/Summability_and_integrability_of_Vilenkin_series">Summability and integrability of Vilenkin 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="43632767" href="https://unsa-ba.academia.edu/Avdispahic">Muharem Avdispahić</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Collectanea Mathematica, 2000</p><p class="ds-related-work--abstract ds2-5-body-sm">A sufficient condition on a triangular matrix Λ=[λ nk ],(n,k∈N 0),λ n0 =1 (∀n∈N 0), is given, in order that f −L n (Λ,f) q →0 (n→∞), for q∈ 1,∞ and an arbitrary function f ∈L q (G), where L n (Λ,f):= n k=0 λ nkf (k)χ k , (n∈N 0), withf(k):= G fχ k , is a sequence of linear operators on L 1 (G) associated to the matrix Λ. This generalizes an earlier result of Blyumin from bounded to general Vilenkin groups. A new integrability class for general Vilenkin groups, larger than the class F * p (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":"Summability and integrability of Vilenkin series","attachmentId":90120330,"attachmentType":"pdf","work_url":"https://www.academia.edu/85415280/Summability_and_integrability_of_Vilenkin_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/85415280/Summability_and_integrability_of_Vilenkin_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="68923999" 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/68923999/On_C_1_summability_for_Vilenkin_like_systems">On (C, 1) summability for Vilenkin-like systems</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">2001</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we give a common generalization of the Walsh, Vilenkin system, the character system of the group of 2-adic (m-adic) integers, the product system of normed coordinate functions for continuous irreducible unitary representations of the coordinate groups of noncommutative Vilenkin groups, the UDMD product systems (defined by F. Schipp) and some other systems. We prove that for integrable functions σ n f → f (n → ∞) a.e., where σ n f is the n-th (C, 1) mean of f. (This with respect to the character system of the group of m-adic integers was a more than 20 years old conjecture of M.H. Taibleson [24, p. 114].) Define the maximal operator σ * f := sup n |σ n f |. We prove that σ * is of type (p, p) for all 1 < p ≤ ∞ and of weak type (1, 1). Moreover, σ * f 1 ≤ c f H , where H is the Hardy 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":"On (C, 1) summability for Vilenkin-like systems","attachmentId":79223373,"attachmentType":"pdf","work_url":"https://www.academia.edu/68923999/On_C_1_summability_for_Vilenkin_like_systems","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/68923999/On_C_1_summability_for_Vilenkin_like_systems"><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="79991377" 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/79991377/On_the_N%C3%B6rlund_means_of_Vilenkin_Fourier_series">On the Nörlund 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="142093004" href="https://independent.academia.edu/Istv%C3%A1nBlahota">István Blahota</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Czechoslovak Mathematical Journal, 2015</p><p class="ds-related-work--abstract ds2-5-body-sm">Institute of Mathematics of the Czech Academy of Sciences provides access to digitized documents strictly for personal use. Each copy of any part of this document must contain these Terms of use.</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 Nörlund means of Vilenkin-Fourier series","attachmentId":86521280,"attachmentType":"pdf","work_url":"https://www.academia.edu/79991377/On_the_N%C3%B6rlund_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/79991377/On_the_N%C3%B6rlund_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="54495503" 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/54495503/On_the_Coefficients_of_Multiple_Series_with_Respect_to_Vilenkin_System">On the Coefficients of Multiple Series with Respect to Vilenkin 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="94628820" href="https://independent.academia.edu/FTulone">Francesco Tulone</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Tatra Mountains Mathematical Publications, 2017</p><p class="ds-related-work--abstract ds2-5-body-sm">We give a sufficient condition for coefficients of double series n,m a n,m χ n,m with respect to Vilenkin system to be convergent to zero when n + m → ∞. This result can be applied to the problem of recovering coefficients of a Vilenkin series from its sum.</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 Coefficients of Multiple Series with Respect to Vilenkin System","attachmentId":70831352,"attachmentType":"pdf","work_url":"https://www.academia.edu/54495503/On_the_Coefficients_of_Multiple_Series_with_Respect_to_Vilenkin_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/54495503/On_the_Coefficients_of_Multiple_Series_with_Respect_to_Vilenkin_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="5" data-entity-id="68924028" 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/68924028/On_the_ae_convergence_of_Fourier_series_on_unbounded_Vilenkin_groups">On the ae convergence of Fourier series on unbounded Vilenkin groups</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">1999</p><p class="ds-related-work--abstract ds2-5-body-sm">It is well known that the 2 n th partial sums of the Walsh-Fourier series of an integrable function converges a.e. to the function. This result has been proved Sto by techniques known in the martingale theory. The author gave purely dyadic harmonic analysis" proof of this in the former volume of this journal G at. The Vilenkin groups are generalizations of the Walsh group. We prove the a.e. convergence S M n f ! f n ! 1; f 2 L 1 G m even in the case when G m is an unbounded Vilenkin group. The nowelty of this proof is that we use techniques, which are elementary in dyadic harmonic analysis. We do not use any technique in martingale theory used in the former proof Sto .</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 ae convergence of Fourier series on unbounded Vilenkin groups","attachmentId":79223028,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924028/On_the_ae_convergence_of_Fourier_series_on_unbounded_Vilenkin_groups","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/68924028/On_the_ae_convergence_of_Fourier_series_on_unbounded_Vilenkin_groups"><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="110444358" 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/110444358/On_almost_everywhere_convergence_of_the_generalized_Marcienkiwicz_means_with_respect_to_two_dimensional_Vilenkin_like_systems">On almost everywhere convergence of the generalized Marcienkiwicz means with respect to two dimensional Vilenkin-like systems</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">Miskolc Mathematical Notes, 2020</p><p class="ds-related-work--abstract ds2-5-body-sm">In this paper we investigate the almost everywhere convergence of two dimensional Marcinkiewicz-like means of two variable integrable functions which is given by t α n f = 1 n n−1 ∑ k=0 S α 1 (|n|, k),α 2 (|n|, k) f (M |n| ≤ n < M |n|+1) and give a sufficient condition for functions α : N 2 → N 2 in order to have the a.e. relation t α n f → f for all f ∈ L 1 (G 2 m) with respect to two dimensional bounded Vilenkin-like systems. Finally, we give an application of the main result with respect to triangular summability of Vilenkin-like-Fourier series.</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 of the generalized Marcienkiwicz means with respect to two dimensional Vilenkin-like systems","attachmentId":108260154,"attachmentType":"pdf","work_url":"https://www.academia.edu/110444358/On_almost_everywhere_convergence_of_the_generalized_Marcienkiwicz_means_with_respect_to_two_dimensional_Vilenkin_like_systems","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/110444358/On_almost_everywhere_convergence_of_the_generalized_Marcienkiwicz_means_with_respect_to_two_dimensional_Vilenkin_like_systems"><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="110444342" 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/110444342/Norm_convergence_of_double_Fourier_series_on_unbounded_Vilenkin_groups">Norm convergence of double Fourier series on unbounded Vilenkin groups</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, 2017</p><p class="ds-related-work--abstract ds2-5-body-sm">We study approximation by rectangular partial sums of double Fourier series on unbounded Vilenkin groups in the spaces C and L1. From these results we obtain criterions of the uniform convergence and L-convergence of double Vilenkin-Fourier series. We also prove that these results are sharp.</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 Fourier series on unbounded Vilenkin groups","attachmentId":108260241,"attachmentType":"pdf","work_url":"https://www.academia.edu/110444342/Norm_convergence_of_double_Fourier_series_on_unbounded_Vilenkin_groups","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/110444342/Norm_convergence_of_double_Fourier_series_on_unbounded_Vilenkin_groups"><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="60326744" 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/60326744/Investigations_with_respect_to_the_maximal_operator_of_Fej%C3%A9r_means_on_Vilenkin_systems">Investigations with respect to the maximal operator of Fejér means on Vilenkin systems</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="142093004" href="https://independent.academia.edu/Istv%C3%A1nBlahota">István Blahota</a></div><p class="ds-related-work--metadata ds2-5-body-xs">2006</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":"Investigations with respect to the maximal operator of Fejér means on Vilenkin systems","attachmentId":73822755,"attachmentType":"pdf","work_url":"https://www.academia.edu/60326744/Investigations_with_respect_to_the_maximal_operator_of_Fej%C3%A9r_means_on_Vilenkin_systems","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/60326744/Investigations_with_respect_to_the_maximal_operator_of_Fej%C3%A9r_means_on_Vilenkin_systems"><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="68924072" 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/68924072/Convergence_and_divergence_of_Fej%C3%A9r_means_of_Fourier_series_on_one_and_two_dimensional_Walsh_and_Vilenkin_groups">Convergence and divergence of Fejér means of Fourier series on one and two-dimensional Walsh and Vilenkin groups</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">It is a highly celebrated issue in dyadic harmonic analysis the pointwise convergence of the Fejér (or (C, 1)) means of functions on the Walsh and Vilenkin groups both in the point of view of one and two dimensional cases. We give a résumé of the very recent developments concerning this matter, propose unsolved problems and throw a glance at the investigation of Vilenkin-like systems too.</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 and divergence of Fejér means of Fourier series on one and two-dimensional Walsh and Vilenkin groups","attachmentId":79223192,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924072/Convergence_and_divergence_of_Fej%C3%A9r_means_of_Fourier_series_on_one_and_two_dimensional_Walsh_and_Vilenkin_groups","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/68924072/Convergence_and_divergence_of_Fej%C3%A9r_means_of_Fourier_series_on_one_and_two_dimensional_Walsh_and_Vilenkin_groups"><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":79223356,"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":79223356,"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_79223356" 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-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":"Convergence of Cesaro means of functions with respect to unbounded Vilenkin systems","attachmentId":79223528,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924043/Convergence_of_Cesaro_means_of_functions_with_respect_to_unbounded_Vilenkin_systems","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" 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href="https://independent.academia.edu/Istv%C3%A1nBlahota">István Blahota</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":"Journal of Inequalities in Pure and Applied Mathematics MAXIMAL OPERATORS OF FEJÉR MEANS OF VILENKIN-FOURIER 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-related-work-grid-card-view-pdf" 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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":"Pointwise convergence of double Vilenkin-Fejér means","attachmentId":79223188,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924000/Pointwise_convergence_of_double_Vilenkin_Fej%C3%A9r_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/68924000/Pointwise_convergence_of_double_Vilenkin_Fej%C3%A9r_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 class="ds-related-work--container js-related-work-sidebar-card" data-collection-position="18" data-entity-id="68924010" 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/68924010/Maximal_operators_of_Fej%C3%A9r_means_of_double_Vilenkin_Fourier_series">Maximal operators of Fejér 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="32476274" href="https://unideb.academia.edu/GyorgyGat">Gyorgy Gat</a></div><p class="ds-related-work--metadata ds2-5-body-xs">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":"Maximal operators of Fejér means of double Vilenkin--Fourier 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href="https://www.academia.edu/5757826/Two_Notes_on_Convergence_and_Divergence_A_E_of_Fourier_Series_with_Respect_to_Some_Orthogonal_Systems">Two Notes on Convergence and Divergence A.E. of Fourier Series with Respect to Some Orthogonal Systems</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="8390841" href="https://independent.academia.edu/GuadalupeJ">Jose Guadalupe</a></div><p class="ds-related-work--metadata ds2-5-body-xs">Proceedings of The American Mathematical Society, 1992</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":"Two Notes on Convergence and Divergence A.E. of Fourier Series with Respect to Some Orthogonal 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