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Infinitesimally Lipschitz functions on metric spaces

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Durand-Cartagena, Estibalitz and Jaramillo Aguado, Jesús Ángel (2013) Infinitesimally Lipschitz functions on metric spaces. Preprint . (Unpublished)

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Official URL: http://arxiv.org/pdf/0901.3236v1.pdf


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Abstract

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 regarding the geometry of X. We also obtain a Banach-Stone theorem in this context. In the case of a metric measure space, we also compare D∞(X) with the Newtonian-Sobolev space N1,∞(X). In particular, if X supports a doubling measure and satisfies a local Poincaré inequality, we obtain that D∞(X) = N1,∞(X).


Item Type:Article
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:28383
Deposited On:16 Feb 2015 10:16
Last Modified:16 Feb 2015 10:16

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