Divergence of spherical general terms of double Fourier series

被引：1

作者：

Getsadze, Rostom ^{[1
]}

机构：

[1] Umea Univ, Dept Math & Math Stat, S-90187 Umea, Sweden

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2006年 / 12卷 / 05期

关键词：

double Fourier series; spherical general terms; divergence almost everywhere;

D O I：

10.1007/s00041-006-6045-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove the following theorem: For arbitrary epsilon > 0 there exists a nonnegative function g is an element of L[0, 1](2) such that supp g subset of [0, epsilon](2) and lim sup(R-->infinity)\Sigma(i2+j2=R2) a(i,j)(g)w(i)(x)w(j)(y)\ = infinity almost everywhere on [0, 1](2), where {w(i) (x)w(j)(y)}(i,j=1)(infinity) = is the double Walsh-Paley system. This statement remains true also for the double trigonometric system.

引用

页码：597 / 604

页数：8