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Mat. Zametki, 1970, Volume 8, Issue 5, Pages 595–606 (Mi mz7007)  

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

Abstract: Best-possible conditions, in S. M. Nikol'skii's classes $H^\alpha_p$, are established for the localization of rectangular (or, as they are sometimes called, Pringsheim) partial sums of multiple trigonometric Fourier series.

Full text: PDF file (917 kB)

English version:
Mathematical Notes, 1970, 8:5, 803–809

Bibliographic databases:

UDC: 517.5
Received: 26.02.1969

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/mz7007}
\mathscinet{http://www.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}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. 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
    2. 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
    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. 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
    5. A. M. D'yachenko, “Rate of Pointwise Approximation of Functions by the Cesàro $(C,\beta)$-Means of Their Fourier Series”, Math. Notes, 88:2 (2010), 198–208  mathnet  crossref  crossref  mathscinet  isi  elib
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