Ferenc Lukacs type theorems in terms of the Abel-Poisson mean of conjugate series

被引：14

作者：

Móricz, F ^{[1
]}

机构：

[1] Univ Szeged, Bolyai Inst, H-6720 Szeged, Hungary

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2003年 / 131卷 / 04期

关键词：

function of bounded variation; induced Borel measure; Fourier series; theorem of Fejer; conjugate series; generalized jump; theorem of Ferenc Lukacs; Abel-Poisson; mean smoothness; Zygmund classes lambda(*) and Lambda(*);

D O I：

10.1090/S0002-9939-02-06669-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A theorem of Ferenc Lukacs determines the generalized jumps of a periodic, Lebesgue integrable function f in terms of the partial sum of the conjugate series to the Fourier series of f. The main aim of this paper is to prove an analogous theorem in terms of the Abel-Poisson mean. We also prove an estimate of the partial derivative (with respect to the angle) of the Abel-Poisson mean of an integrable function F at those points at which F is smooth. Finally, we reveal the intimate relation between these two results.

引用

页码：1243 / 1250

页数：8