Schatten class generalized Volterra companion integral operators

TL;DR

This paper characterizes the Schatten class membership of generalized Volterra companion integral operators on Fock spaces using integrability conditions of their symbols, providing simplified criteria and asymptotic norm estimates.

Contribution

It offers new characterizations of Schatten class membership for these operators via integrability of symbols, simplifying previous conditions and including asymptotic norm estimates.

Findings

Characterization of Schatten class membership via $L^{p/2}$ integrability of Berezin transforms.

Simplified criteria using $L^p$ integrability against super exponentially decreasing weights.

Asymptotic estimates for the Schatten $p$-norms of the 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 $\mathcal{S}_p(\mathcal{F}_\alpha^2)$ 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 a supper exponentially decreasing weights. An asymptotic estimates for the $\mathcal{S}_p(\mathcal{F}_\alpha^2)$ norms of the operators have been also provided.