On the variation of maximal operators of convolution type

被引：42

作者：

Cameiro, Emanuel ^{[1
]}

Svaiter, Benar F. ^{[1
]}

机构：

[1] Inst Matematica Pura & Aplicada, BR-22460 Rio De Janeiro, Brazil

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 2013年 / 265卷 / 05期

关键词：

Maximal functions; Heat flow; Poisson kernel; Sobolev spaces; Regularity; Bounded variation; Discrete operators; SOBOLEV SPACES; REGULARITY; THEOREM;

D O I：

10.1016/j.jfa.2013.05.012

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper we study the regularity properties of two maximal operators of convolution type: the heat flow maximal operator (associated to the Gauss kernel) and the Poisson maximal operator (associated to the Poisson kernel). In dimension d = 1 we prove that these maximal operators do not increase the L-P-variation of a function for any p >= 1, while in dimensions d > 1 we obtain the corresponding results for the L-2-variation. Similar results are proved for the discrete versions of these operators. (C) 2013 Elsevier Inc. All rights reserved.

引用

页码：837 / 865

页数：29

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