Cauchy operator on Bergman space of harmonic functions on unit disk

Abstract

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