L2 boundedness of the Cauchy transform implies L2 boundedness of all Calderón-Zygmund operators associated to odd kernels.
Publicacions Matemàtiques, Tome 48 (2004) no. 2, p. 445-479.
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).
Source:
Zbl
Classification : 47A30, 47B38, 42B20 
@article{PMATES_2004__48_2_41506,
     author = {Xavier Tolsa},
     title = {L2 boundedness of the {Cauchy} transform implies {L2} boundedness of all {Calder\'on-Zygmund} operators associated to odd kernels.},
     journal = {Publicacions Matem\`atiques},
     pages = {445-479},
     volume = {48},
     number = {2},
     year = {2004},
     zbl = {an:1066.42013},
     language = {en},
     url = {https://geodesic-test.mathdoc.fr/item/PMATES_2004__48_2_41506/}
}
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Xavier Tolsa. L2 boundedness of the Cauchy transform implies L2 boundedness of all Calderón-Zygmund operators associated to odd kernels.. Publicacions Matemàtiques, Tome 48 (2004) no. 2, p. 445-479. https://geodesic-test.mathdoc.fr/item/PMATES_2004__48_2_41506/