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Generalized Volterra Companion Operators on Fock Spaces

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Abstract

We characterize the bounded and compact generalized Volterra companion integral operators acting between the standard Fock spaces. We also obtain asymptotic estimates for the norm of these operators in terms of certain Berezin type integral transforms which involve some function theoretic properties of symbols inducing the operators. As a special case, we prove that there exist no nontrivial compact Volterra companion integral and multiplication operators on Fock spaces.

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Authors and Affiliations

  1. Education Faculty, Mathematics section, Stord/Haugesund University College (HSH), Klingenbergvegen 8, 5414, Stord, Norway

    Tesfa Mengestie

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  1. Tesfa Mengestie
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Correspondence to Tesfa Mengestie.

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The author is supported by HSH grant 1244/H15.

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Mengestie, T. Generalized Volterra Companion Operators on Fock Spaces. Potential Anal 44, 579–599 (2016). https://doi.org/10.1007/s11118-015-9520-3

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  • DOI: https://doi.org/10.1007/s11118-015-9520-3

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