Necessary conditions for L1-convergence of double Fourier series

被引：1

作者：

Ferenc Moricz ^{[1
]}

机构：

[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

来源：

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2010年 / 363卷 / 02期

关键词：

Double Fourier series; L-1-convergence; Hardy's inequality for functions in the Hardy space H-1; Bernstein-Zygmund inequalities for the derivatives of trigonometric polynomials in L-1-norm; Conjugate trigonometric polynomials;

D O I：

10.1016/j.jmaa.2009.09.030

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We extend the results of A.S. Belov from single to double Fourier series, which give necessary conditions in terms of the Fourier coefficients for L-1-convergence. Our basic tools are Hardy's inequality for the Taylor coefficients of a function in the Hardy space H-1 on the unit disk. and the Bernstein-Zygmund inequalities for the derivative of a trigonometric polynomial in L-1-norm. (C) 2009 Elsevier Inc. All rights reserved.

引用

页码：559 / 568

页数：10

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