RESISTANCE CONDITIONS, POINCARE INEQUALITIES, THE LIP-LIP CONDITION AND HARDY'S INEQUALITIES

被引：0

作者：

Kinnunen, Juha ^{[1
]}

Silvestre, Pilar ^{[1
]}

机构：

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

来源：

DEMONSTRATIO MATHEMATICA | 2016年 / 49卷 / 01期

基金：

芬兰科学院;

关键词：

capacity; Sobolev-Poincare inequality; Hardy inequality; analysis on metric measure spaces;

D O I：

10.1515/dema-2016-0006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

This note investigates weaker conditions than a Poincare inequality in analysis on metric measure spaces. We discuss two resistance conditions which are stated in terms of capacities. We show that these conditions can be characterized by versions of Sobolev-Poincare inequalities. As a consequence, we obtain so-called Lip-lip condition related to pointwise Lipschitz constants. Moreover, we show that the pointwise Hardy inequalities and uniform fatness conditions are equivalent under an appropriate resistance condition.

引用

页码：50 / 63

页数：14

共 11 条

[1] Stability of parabolic Harnack inequalities on metric measure spaces [J].