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

作     者：Gyrgy GAT Ushangi GOGINAVA 

作者机构：Institute of Mathematics and Computer ScienceCollege of Nyíregyháza Department of Mechanics and MathematicsTbilisi State University 

出 版 物：《Acta Mathematica Sinica,English Series》 (数学学报（英文版）)

年 卷 期：2009年第25卷第6期

页      面：903-916页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：the Hungarian National Foundation for Scientific Research(OTKA)(Grant No.T048780) the Georgian National Foundation for Scientific Research(Grant No.GNSF/ST07/3-171) 

主　　题：Walsh function Norlund logarithmic means a.e. divergence. 

摘      要：It is well known in the literature that the logarithmic means 1/logn ^n-1∑k=1 Sk（f）/k of Walsh or trigonometric Fourier series converge a.e. to the function for each integrable function on the unit interval. This is not the case if we take the partial sums. In this paper we prove that the behavior of the so-called NSrlund logarithmic means 1/logn ^n-1∑k=1 Sk（f）/n-k is closer to the properties of partial sums in this point of view.