Almost Everywhere Convergence of Sequences of Cesàro and Riesz Means of Integrable Functions with Respect to the Multidimensional Walsh System  

作　　者：Gyrgy GT 

机构地区：[1]Institute of Mathematics and Computer Science,College of Nyíregyhza

出　　处：《Acta Mathematica Sinica,English Series》2014年第2期311-322,共12页数学学报（英文版）

基　　金：Supported by project TMOP-4.2.2.A-11/1/KONV-2012-0051

摘　　要：The aim of this paper is to prove the a.e.convergence of sequences of the Cesaro and Riesz means of the Walsh–Fourier series of d variable integrable functions.That is,let a=（a1,...,ad）：N→Nd（d∈P）such that aj（n＋1）≥δsupk≤n aj（k）（j=1,...,d,n∈N）for someδ〉0 and a1（＋∞）=···=ad（＋∞）=＋∞.Then,for each integrable function f∈L1（Id）,we have the a.e.relation for the Cesaro means limn→∞σαa（n）f=f and for the Riesz means limn→∞σα,γa（n）f=f for any 0〈αj≤1≤γj（j=1,...,d）.A straightforward consequence of our result is the so-called cone restricted a.e.convergence of the multidimensional Cesaro and Riesz means of integrable functions,which was proved earlier by Weisz.The aim of this paper is to prove the a.e.convergence of sequences of the Cesaro and Riesz means of the Walsh–Fourier series of d variable integrable functions.That is,let a=（a1,...,ad）：N→Nd（d∈P）such that aj（n＋1）≥δsupk≤n aj（k）（j=1,...,d,n∈N）for someδ〉0 and a1（＋∞）=···=ad（＋∞）=＋∞.Then,for each integrable function f∈L1（Id）,we have the a.e.relation for the Cesaro means limn→∞σαa（n）f=f and for the Riesz means limn→∞σα,γa（n）f=f for any 0〈αj≤1≤γj（j=1,...,d）.A straightforward consequence of our result is the so-called cone restricted a.e.convergence of the multidimensional Cesaro and Riesz means of integrable functions,which was proved earlier by Weisz.

关 键 词：Walsh system d-dimensional Fejer and Riesz means SUBSEQUENCE almost everywhereconvergence 

分 类 号：O174.21[理学—数学]