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Trudy Inst. Mat. i Mekh. UrO RAN, 2005, Volume 11, Number 2, Pages 10–29 (Mi timm186)  

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

Growth rate of sequences of multiple rectangular Fourier sums

N. Yu. Antonov


Abstract: In the case when a sequence of $d$-dimensional vectors $\mathbf n_k=(n_k^1,n_k^2,…,n_k^d)$ with nonnegative integral coordinates satisfies the condition
$$ n_k^j=\alpha_jm_k+O(1),\quad k\in\mathbb N,\quad1\le j\le d, $$
where $\alpha_1…,\alpha_d$ are nonnegative real numbers and $\{m_k\}_{k=1}^\infty$ is a sequence of positive integers, the following estimate of the rate of growth of sequences $S_{\mathbf n_k}(f,\mathbf x)$ of rectangular partial sums of multiple trigonometric Fourier series is obtained: if $f\in L(\ln^+L)^{d-1}([-\pi,\pi)^d)$, then
$$ S_{\mathbf n_k}(f,\mathbf x)=o(\ln k)\quada.e. $$
Analogous estimates are valid for conjugate series as well.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2005, suppl. 2, S9–S29

Bibliographic databases:

UDC: 517.518
Received: 16.01.2005

Citation: N. Yu. Antonov, “Growth rate of sequences of multiple rectangular Fourier sums”, Function theory, Trudy Inst. Mat. i Mekh. UrO RAN, 11, no. 2, 2005, 10–29; Proc. Steklov Inst. Math. (Suppl.), 2005no. , suppl. 2, S9–S29

Citation in format AMSBIB
\Bibitem{Ant05}
\by N.~Yu.~Antonov
\paper Growth rate of sequences of multiple rectangular Fourier sums
\inbook Function theory
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2005
\vol 11
\issue 2
\pages 10--29
\mathnet{http://mi.mathnet.ru/timm186}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2200219}
\zmath{https://zbmath.org/?q=an:1143.42010}
\elib{http://elibrary.ru/item.asp?id=12040700}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2005
\issue , suppl. 2
\pages S9--S29


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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 almost everywhere convergence of sequences of multiple rectangular Fourier sums”, Proc. Steklov Inst. Math. (Suppl.), 264, suppl. 1 (2009), S1–S18  mathnet  crossref  isi  elib
    2. 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
    3. 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
    4. N. Yu. Antonov, “Estimates for the growth order of sequences of multiple rectangular Fourier sums of integrable functions”, J. Math. Sci., 209:1 (2015), 1–11  mathnet  crossref  mathscinet
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