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.

引用

页码：505 / 515

页数：11