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oai:docta.ucm.es:20.500.14352/337882023-08-28T06:12:15Zcom_20.500.14352_14col_20.500.14352_15

Durand-Cartagena, Estibalitz Jaramillo Aguado, Jesús Ángel 2023-06-19T13:28:05Z 2023-06-19T13:28:05Z 2013 https://hdl.handle.net/20.500.14352/33788 http://arxiv.org/pdf/0901.3236v1.pdf http://arxiv.org 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). eng open access Infinitesimally Lipschitz functions on metric spaces journal article