On L-convergence of trigonometric series

被引：17

作者：

Szal, Bogdan ^{[1
]}

机构：

[1] Univ Zielona Gora, Fac Math Comp Sci & Econometr, PL-65516 Zielona Gora, Poland

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2011年 / 373卷 / 02期

关键词：

Trigonometric series; Fourier series; L-convergence; Embedding relations; FOURIER-SERIES; L-1-CONVERGENCE; L1-CONVERGENCE;

D O I：

10.1016/j.jmaa.2010.08.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper we consider the trigonometric series with (beta, r)-general monotone and (beta, r)-rest bounded variation coefficients. Necessary and sufficient conditions of L-convergence for such series are obtained in terms of the coefficients. Moreover, we generalize and extend the Tikhonov results [J. Math. Anal. Appl. 347 (2008) 416-427] to the class GM(beta, r) or the class RBVS(beta, r). (C) 2010 Elsevier Inc. All rights reserved.

引用

页码：449 / 463

页数：15

共 19 条

[1]

Belov A.S., 1998, IZV TUL GOS U MMI, V4, P40

[2] Remarks on mean convergence (boundedness) of partial sums of trigonometric series [J].

Belov, AS .

MATHEMATICAL NOTES, 2002, 71 (5-6) :739-748

[3]

Fridli S, 1997, STUD MATH, V125, P161

[4] L1-CONVERGENCE OF FOURIER-SERIES WITH QUASI-MONOTONE COEFFICIENTS [J].

GARRETT, JW ;

REES, CS ;

STANOJEVIC, CV .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1978, 72 (03) :535-538

[5] A new condition for the uniform convergence of certain trigonometric series [J].

Le, RJ ;

Zhou, SP .

ACTA MATHEMATICA HUNGARICA, 2005, 108 (1-2) :161-169

[6]

Leindler L., 2001, ANAL MATH, V27, P279

[7] L1-CONVERGENCE OF FOURIER-SERIES WITH O-REGULARLY VARYING QUASIMONOTONIC COEFFICIENTS [J].

STANOJEVIC, VB .

JOURNAL OF APPROXIMATION THEORY, 1990, 60 (02) :168-173

[8]

SZAL B, NEW CLASS NUMERICAL

[9]

TELJAKOVSKII SA, 1975, P STEKLOV I MATH, V134, P351

[10]

TELJAKOVSKIL SA, 2003, APPROXIMATION FUNCTI, P240

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