Lebesgue points and Cesaro summability of higher dimensional Fourier series over a cone

被引：1
|
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：
ACTA SCIENTIARUM MATHEMATICARUM | 2021年 / 87卷 / 3-4期
关键词：
Cesaro summability; Hardy-Littlewood maximal function; Lebesgue points; MARCINKIEWICZ-FEJER MEANS; EVERYWHERE CONVERGENCE; PARTIAL-SUMS; TRANSFORMS; RESPECT;
D O I：
10.14232/actasm-021-614-3
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We introduce a new concept of Lebesgue points, the so-called.Lebesgue points, where omega > 0. As a generalization of the classical Lebesgue's theorem, we prove that the Cesaro means sigma(a)(n)f of the Fourier series of a multidimensional function f is an element of L-1(T-d) converge to f at each omega-Lebesgue point (0 < omega < alpha) as n -> 8.
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页码：505 / 515
页数：11
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