A family of singular integral operators which control the Cauchy transform

Petr Chunaev, Joan Mateu, Xavier Tolsa

We study the behaviour of singular integral operators $T_{k_t}$ of convolution type on $\mathbb{C}$ associated with the parametric kernels $$ k_t(z):=\frac{(\Re z)^{3}}{|z|^{4}}+t\…