傅立叶级数的勒贝格点和可和点集合的描述

A. D’yachkov
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引用次数: 1

摘要

一个局部可积函数在欧几里德空间上的勒贝格点的集合是一个满测度的-集合。本文证明了每一个全测度的集合都是某可测有界函数的勒贝格点的集合,并进一步证明了具有这些性质的集合是某可测有界函数的卷积型奇异积分的收敛点和非切(稳定)收敛点的集合。在此结果的基础上,用Abel、Riesz和Picard三种方法描述了多重傅立叶级数的可和点集。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A DESCRIPTION OF THE SETS OF LEBESGUE POINTS AND POINTS OF SUMMABILITY OF A FOURIER SERIES
The set of Lebesgue points of a locally integrable function on -dimensional Euclidean space , , is an -set of full measure. In this article it is shown that every -set of full measure is the set of Lebesgue points of some measurable bounded function, and, further, that a set with these properties is the set of points of convergence and nontangential (stable) convergence of a singular integral of convolution type: for some measurable bounded function . On the basis of this result the set of points of summability of a multiple Fourier series by methods of Abel, Riesz, and Picard types is described.
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