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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).
Tolsa, Xavier. "L2 boundedness of the Cauchy transform implies L2 boundedness of all Calderón-Zygmund operators associated to odd kernels.." Publicacions Matemàtiques 48.2 (2004): 445-479. <http://eudml.org/doc/41506>.
@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 -