L2 boundedness of the Cauchy transform implies L2 boundedness of all Carlderón-Zygmund operators associated to odd kernels
Let µ be a Radon measure on C without atoms. In this paper we prove that if the Cauchy transform is bounded in L2 (µ), then all 1-dimensional Calder'on-Zygmund operators associated to odd and sufficiently smooth kernels are also bounded in L2 (µ).
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2004 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:2042 |
| Acceso en línea: | https://ddd.uab.cat/record/2042 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_48204_09 |
| Access Level: | acceso abierto |
| Palabra clave: | Cauchy transform Calderón-Zygmund operators L2 estimates Corona decomposition Non doubling measures |
| Sumario: | Let µ be a Radon measure on C without atoms. In this paper we prove that if the Cauchy transform is bounded in L2 (µ), then all 1-dimensional Calder'on-Zygmund operators associated to odd and sufficiently smooth kernels are also bounded in L2 (µ). |
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