GEOMETRIC CHARACTERIZATIONS OF p-POINCARE INEQUALITIES IN THE METRIC SETTING

被引：10

作者：

Durand-Cartagena, Estibalitz ^{[1
]}

Jaramillo, Jesus A. ^{[2
]}

Shanmugalingam, Nageswari ^{[3
]}

机构：

[1] UNED, ETSI Ind, Dept Matemat Aplicada, Juan del Rosal 12,Ciudad Univ, Madrid 28040, Spain

[2] Univ Complutense Madrid, Fac CC Matemat, Dept Anal Matemat, E-28040 Madrid, Spain

[3] Univ Cincinnati, Dept Math Sci, POB 210025, Cincinnati, OH 45221 USA

来源：

PUBLICACIONS MATEMATIQUES | 2016年 / 60卷 / 01期

基金：

美国国家科学基金会;

关键词：

p-Poincare inequality; metric measure space; thick quasiconvexity; quasiconvexity; singular doubling measures in R; Lip-lip condition; LIPSCHITZ FUNCTIONS; NEWTONIAN SPACES; SOBOLEV SPACES; MODULUS; DIFFERENTIABILITY; EQUIVALENCE; GRADIENTS;

D O I：

10.5565/PUBLMAT_60116_04

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We prove that a locally complete metric space endowed with a doubling measure satisfies an infinity-Poincare inequality if and only if given a null set, every two points can be joined by a quasiconvex curve which "almost avoids" that set. As an application, we characterize doubling measures on R satisfying an infinity-Poincare inequality. For Ahlfors Q-regular spaces, we obtain a characterization of p-Poincare inequality for p > Q in terms of the p-modulus of quasiconvex curves connecting pairs of points in the space. A related characterization is given for the case Q - 1 < p <= Q.

引用

页码：81 / 111

页数：31

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