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Durand-Cartagena, Estibalitz ; Jaramillo Aguado, Jesús Ángel ; Shanmugalingam, Nageswari | Centre de Recerca Matemàtica | 2009-10We study a geometric characterization of ??Poincaré inequality. We show that a path-connected complete doubling metric measure space supports an ??Poincaré inequality if and only if it is thick quasi-convex. We also prove that these two equivale[...]texto impreso
We study a generalization of classical Poincare inequalities, and study conditions that link such an inequality with the first order calculus of functions in the metric measure space setting when the measure is doubling and the metric is complet[...]texto impreso
Durand-Cartagena, Estibalitz ; Jaramillo Aguado, Jesús Ángel ; Shanmugalingam, Nageswari | Universitat Aut?noma de Barcelona | 2016We 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 [...]texto impreso
For a metric space X, we study the space D?(X) of bounded functions on X whose infinitesimal Lipschitz constant is uniformly bounded. D?(X) is compared with the space LIP?(X) of bounded Lipschitz functions on X, in terms of different properties [...]texto impreso
Durand-Cartagena, Estibalitz ; Jaramillo Aguado, Jesús Ángel | Academic Press Inc Elsevier Science | 2010For a metric space X, we study the space D(infinity)(X) of bounded functions on X whose pointwise Lipschitz constant is uniformly bounded. D(infinity)(X) is compared with the space LIP(infinity)(X) of bounded Lipschitz functions on X, in terms o[...]
