Generalized Localization for Spherical Partial Sums of Multiple Fourier Series

被引：2

作者：

Ashurov, Ravshan ^{[1
,2
]}

机构：

[1] Natl Univ Uzbekistan, Tashkent, Uzbekistan

[2] Uzbek Acad Sci, Inst Math, 81 Mirzo Ulugbek Str, Tashkent 100170, Uzbekistan

来源：

JOURNAL OF FOURIER ANALYSIS AND APPLICATIONS | 2019年 / 25卷 / 06期

关键词：

Multiple Fourier series; Spherical partial sums; Convergence almost-everywhere; Generalized localization;

D O I：

10.1007/s00041-019-09697-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper the generalized localization principle for the spherical partial sums of the multiple Fourier series in the L2-class is proved, that is, if f. L2(TN) and f = 0 on an open set similar to. TN, then it is shown that the spherical partial sums of this function converge to zero almost-everywhere on similar to. It has been previously known that the generalized localization is not valid in L p(TN) when 1 = p < 2. Thus the problem of generalized localization for the spherical partial sums is completely solved in L p(TN), p = 1: if p = 2 then we have the generalized localization and if p < 2, then the generalized localization fails.

引用

页码：3174 / 3183

页数：10

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