Geometric characterizations of p-Poincaré inequalities in the metric setting
Durand-Cartagena, Estibalitz (Universidad Nacional de Educación a Distancia (Espanya). ETSI Industriales)
Jaramillo, Jesús A (Universidad Complutense de Madrid. Departamento de Análisis Matemático y Matemática Aplicada)
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 ; Versió publicada
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 alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/302244
DOI: 10.5565/PUBLMAT_60116_04

31 p, 475.4 KB

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