On convergence of multiple trigonometric series with monotone coefficients

被引：1

作者：

Dzhumabaeva, D. G. ^{[1
]}

Dyachenko, M. I. ^{[2
]}

Nursultanov, E. D. ^{[3
]}

机构：

[1] Gumilev Eurasian Natl Univ, Astana, Kazakhstan

[2] Moscow MV Lomonosov State Univ, Moscow, Russia

[3] Moscow MV Lomonosov State Univ, Kazakh Div, Astana, Kazakhstan

来源：

SIBERIAN MATHEMATICAL JOURNAL | 2017年 / 58卷 / 02期

基金：

俄罗斯基础研究基金会;

关键词：

multiple trigonometric series; Pringsheim convergence; Lebesgue space with mixed metric; monotone coefficients;

D O I：

10.1134/S0037446617020033

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the Pringsheim pointwise convergence of multiple trigonometric series. We obtain a condition on the coefficients of the series that guarantees its Pringsheim convergence and prove the unimprovability of this condition.

引用

页码：205 / 214

页数：10

共 50 条

[21] On the Positivity of Average Sums of Sine Series with Monotone Coefficients
Alferova, E. D.
Popov, A. Yu
MATHEMATICAL NOTES, 2021, 110 (3-4) : 623 - 627
[22] On the Pringsheim Convergence of a Subsequence of Partial Sums of a Fourier Trigonometric Series
S. V. Konyagin
Proceedings of the Steklov Institute of Mathematics, 2022, 319 : S156 - S161
[23] On the Pringsheim convergence of a subsequence of partial sums of a Fourier trigonometric series
Konyagin, Sergei Vladimirovich
TRUDY INSTITUTA MATEMATIKI I MEKHANIKI URO RAN, 2022, 28 (04): : 121 - 127
[24] On the Pringsheim Convergence of a Subsequence of Partial Sums of a Fourier Trigonometric Series
Konyagin, S. V.
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2022, 319 (SUPPL 1) : S156 - S161
[25] Extremal Positivity Problem for Integrals of Sine Series with Monotone Coefficients
Alferova, E. D.
Popov, A. Yu.
MATHEMATICAL NOTES, 2024, 116 (1-2) : 382 - 386
[26] Sets of uniqueness for spherically convergent multiple trigonometric series
Ash, JM
Wang, G
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2002, 354 (12) : 4769 - 4788
[27] On weighted integrability of the sum of series with monotone coefficients with respect to multiplicative systems
Turgumbaev, M. Zh.
Suleimenova, Z. R.
Tungushbaeva, D. I.
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2023, 110 (02): : 160 - 168
[28] Boas-Telyakovskii conditions for the integrability of Multiple Trigonometric Series
Zaderei, P. V.
Pelagenko, E. N.
MATHEMATICAL NOTES, 2008, 84 (3-4) : 584 - 588
[29] Boas-Telyakovskii conditions for the integrability of multiple trigonometric series
P. V. Zaderei
E. N. Pelagenko
Mathematical Notes, 2008, 84 : 584 - 588
[30] Differentiation with Respect to Random Binary Nets and Uniqueness of Multiple Trigonometric Series
Talalyan, A. A.
MATHEMATICAL NOTES, 2010, 88 (1-2) : 79 - 96

← 1 2 3 4 5 →