2026-06-28T15:30:49Zhttps://docta.ucm.es/rest/oai/requestoai:docta.ucm.es:20.500.14352/422882023-08-27T03:55:06Zcom_20.500.14352_14col_20.500.14352_15
Docta Complutense
author
Durand-Cartagena, Estibalitz
author
Jaramillo Aguado, Jesús Ángel
2023-06-20T00:15:38Z
2023-06-20T00:15:38Z
2010
0022-247X
10.1016/j.jmaa.2009.09.039
https://hdl.handle.net/20.500.14352/42288
http://www.sciencedirect.com/science/article/pii/S0022247X0900780X
http://www.sciencedirect.com/
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).
eng
Pointwise Lipschitz functions on metric spaces
journal article
URL
https://docta.ucm.es/bitstreams/817518a8-ca17-46f2-999f-bd9e166d3af3/download
File
MD5
066d938d20a774b55501ae864d40903c
404671
application/pdf
Jaramillo07.pdf