Schatten-class generalized Volterra companion integral operators

Tesfa Mengestie

doi:10.1215/17358787-3492743

April 2016 Schatten-class generalized Volterra companion integral operators

Tesfa Mengestie

Banach J. Math. Anal. 10(2): 267-280 (April 2016). DOI: 10.1215/17358787-3492743

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

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Tesfa Mengestie "Schatten-class generalized Volterra companion integral operators," Banach Journal of Mathematical Analysis 10(2), 267-280, (April 2016). https://doi.org/10.1215/17358787-3492743

Received: 11 April 2015; Accepted: 7 June 2015; Published: April 2016

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