On the regularity of maximal operators

被引：70

作者：

Carneiro, Emanuel ^{[1
]}

Moreira, Diego ^{[2
]}

机构：

[1] Univ Texas Austin, Dept Math, Austin, TX 78712 USA

[2] Univ Iowa, Dept Math, Iowa City, IA 52242 USA

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2008年 / 136卷 / 12期

关键词：

maximal operator; bilinear maximal; Sobolev spaces; weak differentiability; weak continuity;

D O I：

10.1090/S0002-9939-08-09515-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We study the regularity of the bilinear maximal operator when applied to Sobolev functions, proving that it maps W-1,W-p(R) x W-1,W-q(R) -> W-1,W-r(R) with 1 < p, q < infinity and r >= 1, boundedly and continuously. The same result holds on R-n when r > 1. We also investigate the almost everywhere and weak convergence under the action of the classical Hardy-Littlewood maximal operator, both in its global and local versions.

引用

页码：4395 / 4404

页数：10

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