dc.contributor.author |
Durand-Cartagena, Estibalitz |
dc.contributor.author |
Jaramillo, Jesus A. |
dc.contributor.author |
Shanmugalingam, Nageswari |
dc.date |
2016 |
dc.identifier |
https://ddd.uab.cat/record/144963 |
dc.identifier |
urn:10.5565/PUBLMAT_60116_04 |
dc.identifier |
urn:oai:ddd.uab.cat:144963 |
dc.identifier |
urn:oai:raco.cat:article/302244 |
dc.identifier |
urn:articleid:20144350v60n1p81 |
dc.identifier |
urn:scopus_id:85008879503 |
dc.identifier |
urn:wos_id:000373250200004 |
dc.format |
application/pdf |
dc.language |
eng |
dc.publisher |
|
dc.relation |
; |
dc.relation |
Publicacions matemàtiques ; Vol. 60 Núm. 1 (2016), p. 81-111 |
dc.rights |
open access |
dc.rights |
Tots els drets reservats. |
dc.rights |
https://rightsstatements.org/vocab/InC/1.0/ |
dc.subject |
P-Poincaré inequality |
dc.subject |
Metric measure space |
dc.subject |
Thick quasiconvexity |
dc.subject |
Qua- siconvexity |
dc.subject |
Singular doubling measures in R |
dc.subject |
Lip-lip condition |
dc.title |
Geometric characterizations of p-Poincaré inequalities in the metric setting |
dc.type |
Article |
dc.description.abstract |
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. |