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].
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页码：957 / 986
页数：30
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