Cauchy operator on Bergman space of harmonic functions on unit disk

Abstract

We find the exact asymptotic behaviour of singular values of theoperator $CP_h$, where $C$ is the integral Cauchy's operator and $P_h$ integral operator with the kernel$$K\left( z,\zeta\right) =\frac{\left( 1-\vert z\vert^2\vert\zeta\vert^2\right)^2}{\pi\vert 1-z\overline{\zeta }\vert^4}-\frac{2}{\pi }\ \frac{\vert z\vert^2\vert\zeta\vert^2}{\vert 1-z\overline{\zeta }\vert^2}.$$