On the rate of convergence in L of Fourier sine series with monotone coefficients

被引：2

作者：

Telyakovskii, S. A. ^{[1
]}

机构：

[1] Russian Acad Sci, Steklov Math Inst, Moscow, Russia

来源：

MATHEMATICAL NOTES | 2016年 / 100卷 / 3-4期

关键词：

convergence in L; sine series with monotone coefficients;

D O I：

10.1134/S0001434616090145

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It is shown that the exact order of decrease of the norm in L of the remainder of a Fourier sine series with monotone coefficients can be expressed in terms of the coefficients of the series just as for a series with convex coefficients. But the numerical multipliers in the estimates are different.

引用

页码：472 / 476

页数：5

共 50 条

[31] ON THE BEHAVIOR NEAR THE ORIGIN OF DOUBLE SINE SERIES WITH MONOTONE COEFFICIENTS
Krasniqi, Xhevat Z.
[J]. MATHEMATICA BOHEMICA, 2009, 134 (03): : 255 - 273
[32] ON THE BEHAVIOR NEAR THE ORIGIN OF A SINE SERIES WITH COEFFICIENTS OF MONOTONE TYPE
Krasniqi, Xhevat Z.
[J]. INTERNATIONAL JOURNAL OF ANALYSIS AND APPLICATIONS, 2014, 4 (01): : 36 - 44
[33] Estimates of the sums of sine series with monotone coefficients of certain classes
Popov, AY
[J]. MATHEMATICAL NOTES, 2003, 74 (5-6) : 829 - 840
[34] Cosine and sine series with generalized monotone coefficients in Lorentz spaces
S. S. Volosivets
[J]. Analysis Mathematica, 2017, 43 : 641 - 655
[35] Cosine and sine series with generalized monotone coefficients in Lorentz spaces
Volosivets, S. S.
[J]. ANALYSIS MATHEMATICA, 2017, 43 (04) : 641 - 655
[36] Estimate for the Integral of the Absolute Value of a Sine Series with Monotone Coefficients
Popov, A. Yu.
Telyakovskii, S. A.
[J]. PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS, 2013, 280 (01) : 263 - 267
[37] ON DOUBLE COSINE, SINE, AND WALSH-SERIES WITH MONOTONE COEFFICIENTS
MORICZ, F
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 109 (02) : 417 - 425
[38] Estimate for the integral of the absolute value of a sine series with monotone coefficients
A. Yu. Popov
S. A. Telyakovskii
[J]. Proceedings of the Steklov Institute of Mathematics, 2013, 280 : 263 - 267
[39] ON THE UNIFORM-CONVERGENCE OF SINE SERIES WITH QUASIMONOTONE COEFFICIENTS
NURCOMBE, JR
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1992, 166 (02) : 577 - 581
[40] Uniform Convergence of Trigonometric Series with General Monotone Coefficients
Dyachenko, Mikhail
Mukanov, Askhat
Tikhonov, Sergey
[J]. CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2019, 71 (06): : 1445 - 1463

← 1 2 3 4 5 →