Sharp Self-improving Properties of Generalized Orlicz-Poincare Inequalities in Connected Metric Measure Spaces

被引：8

作者：

Heikkinen, Toni ^{[1
]}

机构：

[1] Aalto Univ, Inst Math, FI-00076 Aalto, Finland

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2010年 / 59卷 / 03期

关键词：

Metric measure space; doubling measure; Poincare inequality; Sobolev space; Orlicz space; Sobolev embedding; differentiability; SOBOLEV; DIFFERENTIABILITY; THEOREM;

D O I：

10.1512/iumj.2010.59.3984

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the self-improving properties of generalized Phi-Poincare inequalities in connected metric spaces equipped with a doubling measure. As a consequence we obtain results concerning integrability, continuity and differentiability of Orlicz-Sobolev functions on spaces supporting a Phi-Poincare inequality. Our results are optimal and generalize some of the results of Cianchi [4, 5], Hajlasz and Koskela [9, 10], MacManus and Perez [19], Balogh, Rogovin and Zurcher [2] and Stein [22].

引用

页码：957 / 986

页数：30

共 11 条

[1] Differentiability and Poincare-type inequalities in metric measure spaces
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