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).

Detalles Bibliográficos
Autor: Tolsa Domènech, Xavier|||0000-0001-7976-5433
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
Descripción
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).