In the setting of a metric measure space (X, d, μ) with an n-dimensional Radon measure μ, we give a necessary and sufficient condition for the boundedness of Calderón-Zygmund operators associated to the measure μ on Lipschitz spaces on the support of μ. Also, for the Euclidean space Rd with an arbitrary Radon measure μ, we give several characterizations of Lipschitz spaces on the support of μ, Lip(α,μ), in terms of mean oscillations involving μ. This allows us to view the "regular" BMO space of X. Tolsa as a limit case for α → 0 of the spaces Lip(α,μ).
@article{urn:eudml:doc:41570,
title = {Lipschitz spaces and Calder\'on-Zygmund operators associated to non-doubling measures.},
journal = {Publicacions Matem\`atiques},
volume = {49},
year = {2005},
pages = {285-296},
zbl = {1077.42011},
language = {en},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:41570}
}
García-Cuerva, José; Gatto, A. Eduardo. Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.. Publicacions Matemàtiques, Tome 49 (2005) pp. 285-296. http://gdmltest.u-ga.fr/item/urn:eudml:doc:41570/