$L^2$ boundedness of the Cauchy transform implies $L^2$ boundedness of all Calderón-Zygmund operators associated to odd kernels

Resum

Let $\mu$ be a Radon measure on ${\mathbb C}$ without atoms. In this paper we prove that if the Cauchy transform is bounded in $L^2(\mu)$, then all $1$-dimensional Calderón-Zygmund operators associated to odd and sufficiently smooth kernels are also bounded in $L^2(\mu)$.