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

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 Calder'n-Zygmund operators associated to the measure µ on Lipschitz spaces on the support of µ. Also, for the Euclidean space Rd with an ar...

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Detalles Bibliográficos
Autores: García-Cuerva Abengoza, José, Gatto, A. Eduardo
Tipo de recurso: artículo
Fecha de publicación:2005
País:España
Institución:Universitat Autònoma de Barcelona
Repositorio:Dipòsit Digital de Documents de la UAB
Idioma:inglés
OAI Identifier:oai:ddd.uab.cat:5105
Acceso en línea:https://ddd.uab.cat/record/5105
https://dx.doi.org/urn:doi:10.5565/PUBLMAT_49205_02
Access Level:acceso abierto
Descripción
Sumario: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 Calder'n-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).