Mean bounded variation condition and applications in double trigonometric series

被引：0

作者：

Yu, Dansheng ^{[1
]}

Zhou, Ping ^{[2
]}

Zhou, Songping ^{[3
]}

机构：

[1] Hangzhou Normal Univ, Dept Math, Hangzhou 310036, Zhejiang, Peoples R China

[2] St Francis Xaiver Univ, Dept Math Stat & Comp Sci, Antigonish, NS B2G2W5, Canada

[3] Zhejiang Sci Tech Univ, Inst Math, Hangzhou 310018, Zhejiang, Peoples R China

来源：

ANALYSIS MATHEMATICA | 2012年 / 38卷 / 02期

基金：

加拿大自然科学与工程研究理事会;

关键词：

WEIGHTED INTEGRABILITY; DOUBLE COSINE; L(1)-CONVERGENCE; THEOREM;

D O I：

10.1007/s10476-012-0201-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce a new kind of double sequences named MVBVDS and some new classes of weight functions to study the weighted integrability of the double trigonometric series. Several results of Chen, Marzuq, Mricz, Ram and Singh Bhatia (see [2]-[10]) are generalized and some new results are established.

引用

页码：83 / 104

页数：22

共 13 条

[1] INTEGRABILITY THEOREMS FOR FOURIER SERIES [J].

ASKEY, R ;

WAINGER, S .

DUKE MATHEMATICAL JOURNAL, 1966, 33 (01) :223-&

[2] WEIGHTED INTEGRABILITY AND L(1)-CONVERGENCE OF MULTIPLE TRIGONOMETRIC SERIES [J].

CHEN, CP .

STUDIA MATHEMATICA, 1994, 108 (02) :177-190

[3] Two-parameter Hardy-Littlewood inequality and its variants [J].

Chen, CP ;

Luor, DC .

STUDIA MATHEMATICA, 2000, 139 (01) :9-27

[4]

Dyachenko M., 2008, TOPICS CLASSICAL ANA, P88

[5] A Hardy-Littlewood theorem for multiple series [J].

Dyachenko, Mikhail ;

Tikhonov, Sergey .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 339 (01) :503-510

[6] INTEGRABILITY THEOREM OF MULTIPLE TRIGONOMETRIC SERIES [J].

MARZUQ, MMH .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1991, 157 (02) :337-345

[7] ON DOUBLE COSINE, SINE, AND WALSH-SERIES WITH MONOTONE COEFFICIENTS [J].

MORICZ, F .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 109 (02) :417-425

[8] ON THE INTEGRABILITY AND L1-CONVERGENCE OF DOUBLE TRIGONOMETRIC SERIES [J].

MORICZ, F .

STUDIA MATHEMATICA, 1991, 98 (03) :203-225

[9] ON THE INTEGRABILITY AND L(1)-CONVERGENCE OF DOUBLE TRIGONOMETRIC SERIES .2. [J].

MORICZ, F .

ACTA MATHEMATICA HUNGARICA, 1995, 69 (1-2) :99-110

[10] On weighted integrability of double cosine series [J].

Ram, B ;

Bhatia, SS .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1997, 208 (02) :510-519

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