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Izv. RAN. Ser. Mat., 1995, Volume 59, Issue 2, Pages 129–142 (Mi izv15)  

This article is cited in 4 scientific papers (total in 4 papers)

$u$-convergence of multiple Fourier series

M. I. Dyachenko

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Abstract: The $u$-convergence of multiple Fourier series is studied, generalizing convergence in the Pringsheim sense, with respect to spheres. A definitive condition in terms of moduli of smoothness is found on a functional class that implies the $u$-convergence of Fourier series in the metrics $L_p(T^m)$, where $1\leqslant p\leqslant\infty$, $p\ne 2$ and $m\geqslant 2$.

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English version:
Izvestiya: Mathematics, 1995, 59:2, 353–366

Bibliographic databases:

MSC: 42B05
Received: 15.09.1993

Citation: M. I. Dyachenko, “$u$-convergence of multiple Fourier series”, Izv. RAN. Ser. Mat., 59:2 (1995), 129–142; Izv. Math., 59:2 (1995), 353–366

Citation in format AMSBIB
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\by M.~I.~Dyachenko
\paper $u$-convergence of multiple Fourier series
\jour Izv. RAN. Ser. Mat.
\yr 1995
\vol 59
\issue 2
\pages 129--142
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\zmath{https://zbmath.org/?q=an:0896.42006}
\transl
\jour Izv. Math.
\yr 1995
\vol 59
\issue 2
\pages 353--366
\crossref{https://doi.org/10.1070/IM1995v059n02ABEH000015}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RZ88800006}


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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. M. I. Dyachenko, “Uniform convergence of double Fourier series for classes of functions with anisotropic smoothness”, Math. Notes, 59:6 (1996), 680–686  mathnet  crossref  crossref  mathscinet  zmath  isi
    2. M. I. Dyachenko, “Two-dimensional Waterman classes and $u$-convergence of Fourier series”, Sb. Math., 190:7 (1999), 955–972  mathnet  crossref  crossref  mathscinet  zmath  isi
    3. M. I. Dyachenko, “$U$-Convergence of Fourier Series with Monotone and with Positive Coefficients”, Math. Notes, 70:3 (2001), 320–328  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    4. M. I. Dyachenko, “Uniform Convergence of Hyperbolic Partial Sums of Multiple Fourier Series”, Math. Notes, 76:5 (2004), 673–681  mathnet  crossref  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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