Per citar aquest document: http://ddd.uab.cat/record/144963
Geometric characterizations of p-Poincaré inequalities in the metric setting
Durand-Cartagena, Estibalitz (Universidad Nacional de Educación a Distancia (Espanya). ETSI Industriales)
Jaramillo, Jesus A. (Universidad Complutense de Madrid. Departamento de Análisis Matemático)
Shanmugalingam, Nageswari (University of Cincinnati. Department of Mathematical Sciences)

Data: 2016
Resum: We prove that a locally complete metric space endowed with a doubling measure satisfies an ∞-Poincar´e 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 ∞-Poincaré inequality. For Ahlfors Q-regular spaces, we obtain a characterization of p-Poincaré 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.
Drets: Tots els drets reservats
Llengua: Anglès.
Document: article ; recerca ; publishedVersion
Matèria: P-Poincaré inequality ; Metric measure space ; Thick quasiconvexity ; Qua- siconvexity ; Singular doubling measures in R ; Lip-lip condition
Publicat a: Publicacions matemàtiques, Vol. 60 Núm. 1 (2016) , p. 81-111 (Survey) , ISSN 2014-4350

Adreça original: http://www.raco.cat/index.php/PublicacionsMatematiques/article/view/10.5565-PUBLMAT_60116_04
DOI: 10.5565/10.5565-PUBLMAT_60116_04


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