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Geometric characterizations of p-Poincaré inequalities in the metric setting

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Durand-Cartagena, Estibalitz and Jaramillo Aguado, Jesús Ángel and Shanmugalingam, Nageswari (2016) Geometric characterizations of p-Poincaré inequalities in the metric setting. Publicacions Matem�tiques, 60 (1). pp. 81-111. ISSN 0214-1493

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Official URL: https://ddd.uab.cat/record/144963


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Abstract

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.


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En el año 2013 se publicó el preprint en Report nº 15, el Pdf se puede ver en este registro.

Uncontrolled Keywords:p-Poincare inequality; metric measure space; thick quasiconvexity; quasiconvexity; singular doubling measures in R; Lip-lip condition
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:28378
Deposited On:16 Feb 2015 10:15
Last Modified:13 May 2016 11:00

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