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 Trudy Inst. Mat. i Mekh. UrO RAN, 2015, Volume 21, Number 4, Pages 161–177 (Mi timm1239)

On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$

N. A. Il'yasov

Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku

Abstract: A solution of the problem on the exact order of deviation in the uniform metric of partial cubic sums of multiple trigonometric Fourier series on classes of functions with a given majorant for the total modulus of smoothness of the $l$th order in $L_1(\mathbb{T}^{m})$ is presented, where $l\in \mathbb{N}$, $m\geq 1$.

Keywords: multiple trigonometric Fourier series, partial cubic sums, order of uniform convergence, total modulus of smoothness, exact order of deviation in the uniform metric.

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Bibliographic databases:
UDC: 517.518.475

Citation: N. A. Il'yasov, “On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 161–177

Citation in format AMSBIB
\Bibitem{Ily15} \by N.~A.~Il'yasov \paper On the order of the uniform convergence of partial cubic sums of multiple trigonometric Fourier series on the function classes $H_{1,m}^{l}[\omega]$ \serial Trudy Inst. Mat. i Mekh. UrO RAN \yr 2015 \vol 21 \issue 4 \pages 161--177 \mathnet{http://mi.mathnet.ru/timm1239} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=3468440} \elib{http://elibrary.ru/item.asp?id=25300995} 

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This publication is cited in the following articles:
1. N. A. Ilyasov, “O poryadke ubyvaniya ravnomernykh modulei gladkosti na klassakh periodicheskikh funktsii $H_{p}^{l}[\omega], l\in \mathbb N, 1\le p<\infty$”, Tr. IMM UrO RAN, 23, no. 4, 2017, 162–175
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