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Trudy Inst. Mat. i Mekh. UrO RAN, 2008, Volume 14, Number 3, Pages 3–18 (Mi timm36)  

This article is cited in 3 scientific papers (total in 3 papers)

On the almost everywhere convergence of sequences of multiple rectangular Fourier sums

N. Yu. Antonov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: In the case when a sequence of $d$-dimensional vectors $\mathrm n_k=(n_k^1,n_k^2,…,n_k^d)$ with nonnegative integer coordinates satisfies the condition
$$ n_k^j=\alpha_j m_k+O(1),\quad k\in\mathbb N,\quad1\le j\le d, $$
where $\alpha_1…\alpha_d>0$, а $m_k\in\mathbb N$, $\lim_{k\to\infty}m_k=\infty$, under some conditions on the function $\varphi\colon[0,+\infty)\to[0,+\infty)$, it is proved that, if the trigonometric Fourier series of any function from $\varphi(L)([-\pi,\pi))$ converges almost everywhere, then, for any $d\in\mathbb N$ and all $f\in\varphi(L)(\ln^+L)^{d-1}([-\pi,\pi)d)$, the sequence $S_{\mathrm{n}_k}(f,\mathrm x)$ of the rectangular partial sums of the multiple trigonometric Fourier series of the function $f$, as well as the corresponding sequences of partial sums of all of its conjugate series, converges almost everywhere.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2009, 264, suppl. 1, S1–S18

Bibliographic databases:

UDC: 517.518
Received: 05.05.2008

Citation: N. Yu. Antonov, “On the almost everywhere convergence of sequences of multiple rectangular Fourier sums”, Trudy Inst. Mat. i Mekh. UrO RAN, 14, no. 3, 2008, 3–18; Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S1–S18

Citation in format AMSBIB
\Bibitem{Ant08}
\by N.~Yu.~Antonov
\paper On the almost everywhere convergence of sequences of multiple rectangular Fourier sums
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2008
\vol 14
\issue 3
\pages 3--18
\mathnet{http://mi.mathnet.ru/timm36}
\elib{http://elibrary.ru/item.asp?id=11929741}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2009
\vol 264
\issue , suppl. 1
\pages S1--S18
\crossref{https://doi.org/10.1134/S0081543809050010}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000265511100001}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-65349190777}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. N. Yu. Antonov, “On the growth rate of arbitrary sequences of double rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S14–S20  mathnet  crossref  isi  elib
    2. N. Yu. Antonov, “On almost everywhere convergence for lacunary sequences of multiple rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 43–59  mathnet  crossref  mathscinet  isi  elib
    3. Nikolai Yu. Antonov, “On $\Lambda$-convergence almost everywhere of multiple trigonometric Fourier series”, Ural Math. J., 3:2 (2017), 14–21  mathnet  crossref
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