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...
| Autores: | , |
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| 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 |
| 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). |
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