Schatten classes of integration operators on Dirichlet spaces

Abstract

We address the question of describing the membership to Schatten-Von Neumann ideals ${\mathcal{S}}_p$ of integration operators $(T_{g}f)(z)={\int }_0^{z}f(\zeta )g^{\prime }(\zeta )d\zeta$ acting on Dirichlet type spaces. We also study this problem for multiplication, Hankel and Toeplitz operators. In particular, we provide an extension of Luecking's result on Toeplitz operators.

Accepted for publication in Journal d' Analyse Mathemátique, (2012)