Pointwise Convergence of Cone-like Restricted Two-dimensional Fejér Means of Walsh-Fourier Series

作     者：Gyrgy GT Kroly NAGY 

作者机构：Institute of Mathematics and Computer Sciences College of Nyíregyhza 

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

年 卷 期：2010年第26卷第12期

页      面：2295-2304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：Supported by the Scientific Board of College of Nyiregyhaza 

主　　题：Walsh group Walsh system pointwise convergence Fejer means 

摘      要：For the two-dimensional Walsh system, Gat and Weisz proved the a.e. convergence of Fejer means σnf of integrable functions, where the set of indices is inside a positive cone around the identical function, that is, β^-1≤n1/n2 ≤β is provided with some fixed parameter ~ 〉 1. In this paper we generalize the result of Gat and Weisz. We not only generalize this theorem, but give a necessary and sufficient condition for cone-like sets in order to preserve this convergence property.