Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.

García-Cuerva, José, and Gatto, A. Eduardo. "Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.." Publicacions Matemàtiques 49.2 (2005): 285-296. <http://eudml.org/doc/41570>.

@article{García2005,
abstract = {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).},
author = {García-Cuerva, José, Gatto, A. Eduardo},
journal = {Publicacions Matemàtiques},
keywords = {Integrales singulares; Operadores de Calderón-Zygmund; Espacio de Lipschitz; Medida de Radon; Funciones de oscilación media acotada; non-doubling measures; Calderón-Zygmund theory; singular integrals; BMO},
language = {eng},
number = {2},
pages = {285-296},
title = {Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.},
url = {http://eudml.org/doc/41570},
volume = {49},
year = {2005},
}

TY - JOUR
AU - García-Cuerva, José
AU - Gatto, A. Eduardo
TI - Lipschitz spaces and Calderón-Zygmund operators associated to non-doubling measures.
JO - Publicacions Matemàtiques
PY - 2005
VL - 49
IS - 2
SP - 285
EP - 296
AB - 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).
LA - eng
KW - Integrales singulares; Operadores de Calderón-Zygmund; Espacio de Lipschitz; Medida de Radon; Funciones de oscilación media acotada; non-doubling measures; Calderón-Zygmund theory; singular integrals; BMO
UR - http://eudml.org/doc/41570
ER -