On the maximal operators of Fej,r means with respect to the character system of the group of 2-adic integers in hardy spaces

被引：2

作者：

Gat, G. ^{[1
]}

Nagy, K. ^{[1
]}

机构：

[1] Coll Nyiregyhaza, Nyiregyhaza, Hungary

来源：

MATHEMATICAL NOTES | 2015年 / 98卷 / 1-2期

关键词：

group of 2-adic integers; character system; Fejer mean; Fourier series; Hardy space; maximal operator; EVERYWHERE CONVERGENCE; FEJER MEANS;

D O I：

10.1134/S0001434615070068

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

It was a question of Taibleson, open for a long time that the almost everywhere convergence of Fej,r (or (C, 1)) means of Fourier series of integrable functions with respect the character system of the group of 2-adic integers. This question was answered by Ga t in 1997. The aim of this paper is to investigate the maximal operator of the sup (n) |sigma (n) |. Among other things, we prove that this operator is bounded from the Hardy space H (p) to the Lebesgue space L (p) if and only if 1/2 < p < a. The two-dimensional maximal operator is also discussed.

引用

页码：68 / 77

页数：10

共 13 条

[1] Pointwise convergence of double Vilenkin-Fejer means [J].