## Banach Journal of Mathematical Analysis

### Schatten-class generalized Volterra companion integral operators

Tesfa Mengestie

#### 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.

#### Article information

Source
Banach J. Math. Anal., Volume 10, Number 2 (2016), 267-280.

Dates
Received: 11 April 2015
Accepted: 7 June 2015
First available in Project Euclid: 15 March 2016

Permanent link to this document
https://projecteuclid.org/euclid.bjma/1458053862

Digital Object Identifier
doi:10.1215/17358787-3492743

Mathematical Reviews number (MathSciNet)
MR3474839

Zentralblatt MATH identifier
1341.47026

#### Citation

Mengestie, Tesfa. Schatten-class generalized Volterra companion integral operators. Banach J. Math. Anal. 10 (2016), no. 2, 267--280. doi:10.1215/17358787-3492743. https://projecteuclid.org/euclid.bjma/1458053862

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