Schatten-class generalized Volterra companion integral operators

Abstract

We study the Schatten-class membership of generalized Volterra companion integral operators on the standard Fock spaces ${\mathcal{F}}_{\alpha }^2$. The Schatten ${\mathcal{S}}_p\left({\mathcal{F}}_{\alpha }^2\right)$ membership of the operators are characterized in terms of $L^{p/2}$-integrability of certain generalized Berezin-type integral transforms on the complex plane. We also give a more simplified and easy-to-apply description in terms of $L^p$-integrability of the symbols inducing the operators against super-exponentially decreasing weights. Asymptotic estimates for the ${\mathcal{S}}_p\left({\mathcal{F}}_{\alpha }^2\right)$ norms of the operators have also been provided.