Toeplitz and Hankel Operators on Bergman Spaces

Let \(\varphi \) be a regular subharmonic weight on the unit disc and let \(A^2_{\omega _\varphi }\) be the weighted Bergman space associated with \(\omega _\varphi (z) = e^{-2\varphi (z)}\). We consider compact Hankel operators \(H_{\overline{\phi }}\), with conjugate analytic symbols \({\overline{\phi }}\), acting on \(A^2_{\omega _\varphi }\). We give a lower and an upper estimates of the trace of \(h(|H_{\overline{\phi }}|)\), where h is a convex function . Next, we give asymptotic estimates of their singular values. We also consider the similar problem for Toeplitz operators.