Banach Journal of Mathematical Analysis

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 Fα2. The Schatten Sp(Fα2) membership of the operators are characterized in terms of Lp/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 Lp-integrability of the symbols inducing the operators against super-exponentially decreasing weights. Asymptotic estimates for the Sp(Fα2) 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

Subjects
Primary: 47B32: Operators in reproducing-kernel Hilbert spaces (including de Branges, de Branges-Rovnyak, and other structured spaces) [See also 46E22]
Secondary: 46E22: Hilbert spaces with reproducing kernels (= [proper] functional Hilbert spaces, including de Branges-Rovnyak and other structured spaces) [See also 47B32] 46E20: Hilbert spaces of continuous, differentiable or analytic functions 47B33: Composition operators

Keywords
Fock space Schatten class Berezin transform Volterra operator generalized Volterra companion operator

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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