Durand-Cartagena, EstibalitzJaramillo Aguado, Jesús Ángel2023-06-202023-06-2020100022-247X10.1016/j.jmaa.2009.09.039https://hdl.handle.net/20.500.14352/42288For 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).engjournal articlehttp://www.sciencedirect.com/science/article/pii/S0022247X0900780Xhttp://www.sciencedirect.com/restricted access517.98Lipschitz functionsBanach–Stone theoremMetric measure spacesNewtonian–Sobolev spacesAnálisis funcional y teoría de operadores