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[{"id":79223361,"identifier":"Attachment_79223361","shouldShowBulkDownload":false}]; window.loswp.shouldDetectTimezone = true; window.loswp.shouldShowBulkDownload = true; window.loswp.showSignupCaptcha = false window.loswp.willEdgeCache = false; window.loswp.work = {"work":{"id":68924109,"created_at":"2022-01-20T22:06:08.110-08:00","from_world_paper_id":192735840,"updated_at":"2024-11-25T03:18:29.847-08:00","_data":{"publisher":"Springer Nature","grobid_abstract":"In 1939 Marcinkiewicz and Zygmund[4] proved that the Fejér means σ 1 n f of the trigonometric Fourier series of two variable integrable functions converge almost everywhere to the function if the ratio of the indices of the means remain in some positive cone around the identical function as they tend to infinity. Numerous results were published concerning Fejér and Cesàro means of Fourier series with respect to the characters of the 2-adic additive group. In 1997 Gát[2] proved the a.e. convergence σ 1 n f → f for integrable functions f. Gát[1] proved the a.e. convergence of Cesáro means σ α n f → f for integrable functions f and α \u003e 0. Now we will demonstrate this theorem for two-dimensional functions. We follow the notions of Schipp-Simon-Wade[6]. Let N denote the set of natural numbers, P := N \\ {0}, and I := [0, 1) the unit interval. Consider the cartesian products N 2 := N × N and I 2 := I × I, that is the collection of integral lattice points in the first quadrant and the unit square. Denote the 1-and 2-dimensional Haar measure of subsets E ⊆ I and F ⊆ I 2 by µ(E) = |E| and µ 2 (F) = |F |. Denote the L p-norm of any function f ∈ L p (I) or f ∈ L p (I 2) by f p. Set I := {[p/2 n , (p + 1)/2 n) | p, n ∈ N, 0 ≤ p \u003c 2 n } the set of dyadic intervals. Given n ∈ N and x ∈ [0, 1) let I n (x) denote the dyadic interval of length 2 −m which contains x. Let I 2 := {I 2 = I 1 × I 2 | I 1 , I 2 ∈ I, |I 1 | = |I 2 |} denote the collection of dyadic squares. Given x = (x 1 , x 2) ∈ I 2 and m ∈ N the dyadic square of area 2 −2m containing x is given by I m (x 1) × I m (x 2) =: I m (x). Also use the notation I n := I n (0) (n ∈ N). The","publication_name":"Acta Mathematica Hungarica","grobid_abstract_attachment_id":"79223361"},"document_type":"paper","pre_hit_view_count_baseline":null,"quality":"high","language":"en","title":"Almost everywhere $${(C, \\alpha, \\beta \u003e 0)}$$ ( C , α , β \u003e 0 ) -summability of the Fourier series of functions on the 2-adic additive group","broadcastable":true,"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.loswp.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 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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, 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":"Triangular Fejér summability of two-dimensional Walsh-Fourier series","attachmentId":79223382,"attachmentType":"pdf","work_url":"https://www.academia.edu/68924070/Triangular_Fej%C3%A9r_summability_of_two_dimensional_Walsh_Fourier_series","alternativeTracking":true}"><span class="material-symbols-outlined" style="font-size: 18px" translate="no">download</span><span class="ds2-5-text-link__content">Download free PDF</span></button><a class="ds2-5-text-link ds2-5-text-link--inline js-related-work-grid-card-view-pdf" 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Mathematicarum</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 summability of Fourier series and the classes H ω","attachmentId":92651302,"attachmentType":"pdf","work_url":"https://www.academia.edu/88731464/On_the_strong_summability_of_Fourier_series_and_the_classes_H_%CF%89","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/88731464/On_the_strong_summability_of_Fourier_series_and_the_classes_H_%CF%89"><span class="ds2-5-text-link__content">View PDF</span><span class="material-symbols-outlined" style="font-size: 18px" 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