Walsh-Lebesgue points of multi-dimensional functionsО точках Уолща-Лебега функций нескольких переменных

被引：0
作者：
Ferenc Weisz
机构：
[1] Eötvös L. University,Department of Numerical Analysis
来源：
Analysis Mathematica | 2008年 / 34卷
关键词：
Fourier Series; Hardy Space; Summability Method; Lebesgue Point; Dyadic Interval;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
Walsh-Lebesgue points are introduced for higher dimensions and it is proved that a.e. point is a Walsh-Lebesgue point of a function f from the Hardy space H1i[0, 1)d, where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ H_1^i [0,1]^d \supset L(\log L)^{d - 1} [0,1)^d for all i = 1,...,d $$\end{document}. Every function f ∈ H1i[0, 1)d is Fejér summable at each Walsh-Lebesgue point. Similar theorem is verified for ϑ-summability.
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页码：307 / 324
页数：17
相关论文
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