Durand-Cartagena, EstibalitzJaramillo Aguado, Jesús Ángel2023-06-192023-06-192013https://hdl.handle.net/20.500.14352/33788For 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).engjournal articlehttp://arxiv.org/pdf/0901.3236v1.pdfhttp://arxiv.orgopen access517.9Análisis funcional y teoría de operadores