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Matematicheskie Zametki, 1970, Volume 8, Issue 5, Pages 595–606 (Mi mzm7007)  
This article is cited in 5 scientific papers (total in 5 papers)

Conditions for the localization of partial sums of S. M. Nikol'skii's class of multiple trigonometric Fourier series

V. A. Il'in

M. V. Lomonosov Moscow State University
Full-text PDF (917 kB) Citations (5)
Abstract: Best-possible conditions, in S. M. Nikol'skii's classes Hpα, are established for the localization of rectangular (or, as they are sometimes called, Pringsheim) partial sums of multiple trigonometric Fourier series.
Received: 26.02.1969
English version:
Mathematical Notes, 1970, Volume 8, Issue 5, Pages 803–809
DOI: https://doi.org/10.1007/BF01146936
Bibliographic databases:
Document Type: Article
UDC: 517.5
Language: Russian
Citation: V. A. Il'in, “Conditions for the localization of partial sums of S. M. Nikol'skii's class of multiple trigonometric Fourier series”, Mat. Zametki, 8:5 (1970), 595–606; Math. Notes, 8:5 (1970), 803–809
Citation in format AMSBIB
\Bibitem{Ili70}
\by V.~A.~Il'in
\paper Conditions for the localization of partial sums of S.\,M.~Nikol'skii's class of multiple trigonometric Fourier series
\jour Mat. Zametki
\yr 1970
\vol 8
\issue 5
\pages 595--606
\mathnet{http://mi.mathnet.ru/mzm7007}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=276687}
\zmath{https://zbmath.org/?q=an:0216.39701|0212.09503}
\transl
\jour Math. Notes
\yr 1970
\vol 8
\issue 5
\pages 803--809
\crossref{https://doi.org/10.1007/BF01146936}
Linking options:
  • https://www.mathnet.ru/eng/mzm7007
  • https://www.mathnet.ru/eng/mzm/v8/i5/p595
    • This publication is cited in the following 5 articles:
    1. A. M. D'yachenko, “Rate of Pointwise Approximation of Functions by the Cesàro (C,β)-Means of Their Fourier Series”, Math. Notes, 88:2 (2010), 198–208  mathnet  crossref  crossref  mathscinet  isi  elib
    2. M. I. Dyachenko, “Some problems in the theory of multiple trigonometric series”, Russian Math. Surveys, 47:5 (1992), 103–171  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    3. Sh. A. Alimov, V. A. Il'in, E. M. Nikishin, “Convergence problems of multiple trigonometric series and spectral decompositions. I”, Russian Math. Surveys, 31:6 (1976), 29–86  mathnet  crossref  mathscinet  zmath
    4. L. V. Zhizhiashvili, “Some problems in the theory of simple and multiple trigonometric and orthogonal series”, Russian Math. Surveys, 28:2 (1973), 65–127  mathnet  crossref  mathscinet  zmath
    5. N. Ch. Krutitskaya, “Best possible localization conditions for rectangular Cesáro means and Abel means in restricted summability of a multiple trigonometric Fourier series in Liouville classes”, Math. USSR-Izv., 7:3 (1973), 589–599  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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