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Pointwise Lipschitz functions on metric spaces

Durand-Cartagena, E. and Jaramillo Aguado, Jesús Ángel (2010) Pointwise Lipschitz functions on metric spaces. Journal of Mathematical Analysis and Applications, 363 (2). pp. 525-548. ISSN 0022-247X

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Abstract

For 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 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(infinity)(X) with the Newtonian-Sobolev space N(1,infinity)(X). In particular, if X Supports a doubling measure and satisfies a local Poincare inequality, we obtain that D(infinity)(X) = N(1,infinity)(X).

Item Type:Article
Uncontrolled Keywords:Lipschitz functions; Banach–Stone theorem; Metric measure spaces; Newtonian–Sobolev spaces
Subjects:Sciences > Mathematics > Functional analysis and Operator theory
ID Code:16235
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Deposited On:10 Sep 2012 10:58
Last Modified:07 Feb 2014 09:25

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