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

共 50 条

[31] Convergence of Multiple Fourier Series of Functions of Bounded Generalized Variation
U. Goginava
A. Sahakian
Ukrainian Mathematical Journal, 2015, 67 : 186 - 198
[32] Strong Convergence of Two-Dimensional Walsh–Fourier Series
G. Tephnadze
Ukrainian Mathematical Journal, 2013, 65 : 914 - 927
[33] Convergence and localization of multiple Fourier series for classes of bounded Λ-variation
Bakhvalov A.N.
Moscow University Mathematics Bulletin, 2008, 63 (3) : 85 - 91
[34] Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space L2((a, b) × (c, d); p(x)q(y))
V. A. Abilov
M. K. Kerimov
Computational Mathematics and Mathematical Physics, 2009, 49 : 1298 - 1302
[35] Sharp estimates for the convergence rate of double Fourier series in terms of orthogonal polynomials in the space L 2((a, b) x (c, d); p(x)q(y))
Abilov, V. A.
Kerimov, M. K.
COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2009, 49 (08) : 1298 - 1302
[36] On the divergence of double Fourier–Walsh and Fourier–Walsh–Kaczmarz series of continuous functions
R. Getsadze
Acta Mathematica Hungarica, 2021, 164 : 51 - 65
[37] Waterman classes and triangular sums of double Fourier series
Bakhvalov A.N.
Analysis Mathematica, 2001, 27 (1) : 3 - 36
[38] Lebesgue points of double Fourier series and strong summability
Weisz, Ferenc
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2015, 432 (01) : 441 - 462
[39] On the strong logarithmic summability of the double trigonometric Fourier series
Getsadze, Rostom
ACTA SCIENTIARUM MATHEMATICARUM, 2011, 77 (3-4): : 473 - 488
[40] On the strong logarithmic summability of the double trigonometric Fourier series
Rostom Getsadze
Acta Scientiarum Mathematicarum, 2011, 77 (3-4): : 473 - 488

← 1 2 3 4 5 →