On the Divergence of N(?)rlund Logarithmic Means of Walsh-Fourier Series

被引：3

作者：

Gyrgy GAT ^{[1
]}

Ushangi GOGINAVA ^{[2
]}

机构：

[1] Institute of Mathematics and Computer Science,College of Nyíregyháza

[2] Department of Mechanics and Mathematics,Tbilisi State University

来源：

Acta Mathematica Sinica(English Series) | 2009年 / 25卷 / 06期

关键词：

Walsh function; Nrlund logarithmic means; a.e; divergence;

D O I：

暂无

中图分类号：

O174.21 [正交级数（傅里叶级数）];

学科分类号：

070104 ;

摘要：

It is well known in the literature that the logarithmic meansof Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function onthe unit interval. This is not the case if we take the partial sums. In this paper we prove that thebehavior of the so-called Norlund logarithmic meansis closer to the properties of partial sums in this point of view.

引用

页码：903 / 916

页数：14

共 5 条

[1] CONVERGENCE OF LOGARITHMIC MEANS OF MULTIPLE WALSH-FOURIER SERIES
G.Gát
U.Goginava
G.Tkebuchava
[J]. Analysis in Theory and Applications, 2005, (04) : 326 - 338
[2] G. Gát,U. Goginava.Uniform and <Emphasis Type="Italic">L–convergence of Logarithmic Means of Walsh–Fourier Series[J].Acta Mathematica Sinica, English Series,2006
[3] Feng Dai,Kun Yang Wang.Summability of Fourier-Laplace Series with the Method of Lacunary Arithmetical Means at Lebesgue Points[J].Acta Mathematica Sinica, English Series,2001
[4] F. Schipp.On boundedly divergent Walsh-Fourier series[J].Acta Mathematica Hungarica,1990(3)
[5] P. Simon.On the divergence of Vilenkin-Fourier series[J].Acta Mathematica Hungarica,1983(3)

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