L2 boundedness of the Cauchy transform implies L2 boundedness of all Calderón-Zygmund operators associated to odd kernels.

@article{Tolsa2004,
abstract = {Let m be a Radon measure on C without atoms. In this paper we prove that if the Cauchy transform is bounded in L2(m), then all 1-dimensional Calderón-Zygmund operators associated to odd and sufficiently smooth kernels are also bounded in L2(m).},
author = {Tolsa, Xavier},
journal = {Publicacions Matemàtiques},
keywords = {Integrales singulares; Operadores de Calderón-Zygmund; Integral de Cauchy; Operadores acotados; Medida de Radon; Cauchy transform; Calderón-Zygmund operator; estimate; corona decomposition; non doubling measure; boundedness},
language = {eng},
number = {2},
pages = {445-479},
title = {L2 boundedness of the Cauchy transform implies L2 boundedness of all Calderón-Zygmund operators associated to odd kernels.},
url = {http://eudml.org/doc/41506},
volume = {48},
year = {2004},
}

TY - JOUR
AU - Tolsa, Xavier
TI - L2 boundedness of the Cauchy transform implies L2 boundedness of all Calderón-Zygmund operators associated to odd kernels.
JO - Publicacions Matemàtiques
PY - 2004
VL - 48
IS - 2
SP - 445
EP - 479
AB - Let m be a Radon measure on C without atoms. In this paper we prove that if the Cauchy transform is bounded in L2(m), then all 1-dimensional Calderón-Zygmund operators associated to odd and sufficiently smooth kernels are also bounded in L2(m).
LA - eng
KW - Integrales singulares; Operadores de Calderón-Zygmund; Integral de Cauchy; Operadores acotados; Medida de Radon; Cauchy transform; Calderón-Zygmund operator; estimate; corona decomposition; non doubling measure; boundedness
UR - http://eudml.org/doc/41506
ER -