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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 3, Pages 55–59 (Mi timm720)  

Note on estimates for the growth order of sequences of multiple rectangular Fourier sums

N. Yu. Antonovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences
b Ural Federal University

Abstract: Let $\{S_{\mathbf n_k}(f,\mathbf x)\}_{k=1}^\infty$ be some sequence of rectangular partial sums of the multiple trigonometric Fourier series of a function $f$, and let $\{\lambda_k\}_{k=1}^\infty$ be a nondecreasing sequence of positive numbers. We investigate conditions on the belonging of the function $f$ to the classes $\varphi (L)$ under which estimates of the following form are possible:
$$ S_{\mathbf n_k}(f,\mathbf x)=o(\lambda_k )\quada.e. $$
where the right-hand side depends on $k$ only.

Keywords: multiple trigonometric Fourier series, growth order estimates.

Full text: PDF file (132 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, 277, suppl. 1, 4–8

Bibliographic databases:

UDC: 517.518
Received: 30.03.2011

Citation: N. Yu. Antonov, “Note on estimates for the growth order of sequences of multiple rectangular Fourier sums”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 3, 2011, 55–59; Proc. Steklov Inst. Math. (Suppl.), 277, suppl. 1 (2012), 4–8

Citation in format AMSBIB
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\by N.~Yu.~Antonov
\paper Note on estimates for the growth order of sequences of multiple rectangular Fourier sums
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2011
\vol 17
\issue 3
\pages 55--59
\mathnet{http://mi.mathnet.ru/timm720}
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\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2012
\vol 277
\issue , suppl. 1
\pages 4--8
\crossref{https://doi.org/10.1134/S0081543812050021}
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