%0 Journal Article
%A Durand-Cartagena, Estibalitz
%A Jaramillo Aguado, Jesús Ángel
%T Infinitesimally Lipschitz functions on metric spaces
%D 2013
%U https://hdl.handle.net/20.500.14352/33788
%X 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).
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