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Trudy Inst. Mat. i Mekh. UrO RAN, 2010, Volume 16, Number 4, Pages 31–37 (Mi timm638)  

This article is cited in 2 scientific papers (total in 2 papers)

On the growth rate of arbitrary sequences of double rectangular Fourier sums

N. Yu. Antonov

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

Abstract: The theorem is proved that an arbitrary sequence $\{S_{m_k,n_k}(f,x,y)\} _{k=1}^\infty$ of double rectangular Fourier sums of any function from the class $L(\ln^+L)^2([0,2\pi)^2)$ satisfies almost everywhere the relation $S_{m_k,n_k}(f,x,y)=o(\ln k)$.

Keywords: multiple trigonometric Fourier series, almost everywhere convergence.

Full text: PDF file (150 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2011, 273, suppl. 1, S14–S20

Bibliographic databases:

UDC: 517.518
Received: 30.11.2009

Citation: N. Yu. Antonov, “On the growth rate of arbitrary sequences of double rectangular Fourier sums”, Trudy Inst. Mat. i Mekh. UrO RAN, 16, no. 4, 2010, 31–37; Proc. Steklov Inst. Math. (Suppl.), 273, suppl. 1 (2011), S14–S20

Citation in format AMSBIB
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\by N.~Yu.~Antonov
\paper On the growth rate of arbitrary sequences of double rectangular Fourier sums
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2010
\vol 16
\issue 4
\pages 31--37
\mathnet{http://mi.mathnet.ru/timm638}
\elib{http://elibrary.ru/item.asp?id=15318485}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2011
\vol 273
\issue , suppl. 1
\pages S14--S20
\crossref{https://doi.org/10.1134/S0081543811050026}
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\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79959236887}


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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. N. Yu. Antonov, “Note on estimates for the growth order of sequences of multiple rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 4–8  mathnet  crossref  isi  elib
    2. N. Yu. Antonov, “O poryadke rosta posledovatelnostei dvoinykh pryamougolnykh summ Fure funktsii iz klassov $\varphi(L)$”, Tr. IMM UrO RAN, 18, no. 4, 2012, 26–34  mathnet  elib
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