RT Journal Article
T1 Pointwise Lipschitz functions on metric spaces
A1 Durand-Cartagena, Estibalitz
A1 Jaramillo Aguado, Jesús Ángel
AB 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).
PB Academic Press Inc Elsevier Science
SN 0022-247X
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/42288
UL https://hdl.handle.net/20.500.14352/42288
LA eng
NO DGES (Spain)
DS Docta Complutense
RD 7 abr 2025