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Sbornik: Mathematics, 2013, Volume 204, Issue 3, Pages 307–322
DOI: https://doi.org/10.1070/SM2013v204n03ABEH004302
(Mi sm8118)
 

This article is cited in 11 scientific papers (total in 11 papers)

On a class of summability methods for multiple Fourier series

M. I. Dyachenko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
References:
Abstract: The paper shows that the same properties which hold for the classical $(C,1)$-means are preserved for a sufficiently large class of summability methods for multiple Fourier series involving rectangular partial sums. More precisely, Fourier series of continuous functions are uniformly summable by these methods, and Fourier series of functions from the class $L (\ln^+ L)^{m-1}(T^m)$ are summable almost everywhere.
Bibliography: 6 titles.
Keywords: multiple Fourier series, summability methods, generalized Cesàro means.
Received: 11.03.2012 and 24.11.2012
Bibliographic databases:
Document Type: Article
UDC: 517.52
MSC: 42A24, 40G05
Language: English
Original paper language: Russian
Citation: M. I. Dyachenko, “On a class of summability methods for multiple Fourier series”, Sb. Math., 204:3 (2013), 307–322
Citation in format AMSBIB
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\by M.~I.~Dyachenko
\paper On a class of summability methods for multiple Fourier series
\jour Sb. Math.
\yr 2013
\vol 204
\issue 3
\pages 307--322
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Linking options:
  • https://www.mathnet.ru/eng/sm8118
  • https://doi.org/10.1070/SM2013v204n03ABEH004302
  • https://www.mathnet.ru/eng/sm/v204/i3/p3
  • This publication is cited in the following 11 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математический сборник Sbornik: Mathematics
    Statistics & downloads:
    Abstract page:856
    Russian version PDF:247
    English version PDF:14
    References:92
    First page:66
     
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