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arXiv · 1507.03536

Schatten class generalized Volterra companion integral operators

Tesfa Mengestie
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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.

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Tesfa Mengestie. 2015-07-13. Schatten class generalized Volterra companion integral operators. https://doi.org/10.1215/17358787-3492743

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