Unrestricted Cesàro summability of d-dimensional Fourier series and Lebesgue points

被引：7
|
作者：
Weisz, Ferenc [1 ]
机构：
[1] Eotvos L Univ, Dept Numer Anal, Pazmany P Setany 1-C, H-1117 Budapest, Hungary
来源：
CONSTRUCTIVE MATHEMATICAL ANALYSIS | 2021年 / 4卷 / 02期
关键词：
Cesaro summability; strong Hardy-Littlewood maximal function; strong Lebesgue points; MARCINKIEWICZ-FEJER MEANS; EVERYWHERE CONVERGENCE; RESPECT;
D O I：
10.33205/cma.859583
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We generalize the classical Lebesgue's theorem to multi-dimensional functions. We prove that the Ces & agrave;ro means of the Fourier series of the multi-dimensional function f is an element of L-1(logL)(d-1)(T-d)superset of L-p(T-d)(1<p <=infinity) converge to f at each strong Lebesgue point.
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页码：179 / 185
页数：7
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