A Covering Lemma on the Unit Sphere and Application to the Fourier-Laplace Convergence

被引：0

作者：

Rong HUANG ^{[1
]}

Kun Yang WANG ^{[2
]}

机构：

[1] Department of Mathematics,Tianjin Normal University

[2] School of Mathematical Sciences,Beijing Normal University

来源：

ActaMathematicaSinica(EnglishSeries) | 2007年 / 23卷 / 07期

关键词：

sphere; covering lemma; Fourier-Laplace series; a.e.convergence;

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：

A covering lemma on the unit sphere is established and then is applied to establish analmost everywhere convergence test of Marcinkiewicz type for the Fourier-Laplace series on the unitsphere which can be stated as follows:Theorem Suppose f ∈ L(∑),n≥3.If f satisfies the conditionat every point x in a set E of positive measure in ∑,then the Cesáro means of critical order(n-2)/2of the Fourier-Laplace series of f converge to f at almost every point x in E.

引用

页码：1327 / 1332

页数：6