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Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞

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Durand-Cartagena, Estibalitz and Jaramillo Aguado, Jesús Ángel and Shanmugalingam, Nageswari (2009) Connections between ∞-Poincaré inequality, quasi-convexity, and N1,∞. Prepublicacions del Centre de Recerca Matemàtica (895). (Unpublished)

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Official URL: http://www.recercat.cat/bitstream/handle/2072/47933/Pr895.pdf?sequence=1




Abstract

We 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 equivalent properties are also equivalent to the purely analytic property that N1,∞(X) = LIP∞(X), where LIP∞(X) is the collection of bounded Lipschitz functions on X and N1,∞(X) is the Newton-Sobolev space studied in [DJ].


Item Type:Article
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:28477
Deposited On:20 Feb 2015 11:35
Last Modified:01 Feb 2016 14:49

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