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Hilbert–Schmidt Hankel Operators over Complete Reinhardt Domains

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Abstract

Let \({\mathcal{R}}\) be an arbitrary bounded complete Reinhardt domain in \({\mathbb{C}^n}\). We show that for \({n \geq 2}\), if a Hankel operator with an anti-holomorphic symbol is Hilbert–Schmidt on the Bergman space \({A^2(\mathcal{R})}\), then it must equal zero. This fact has previously been proved only for strongly pseudoconvex domains and for a certain class of pseudoconvex domains.

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  1. Department of Mathematics and Statistics, Mail Stop 942, University of Toledo, Toledo, OH, 43606, USA

    Trieu Le

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  1. Trieu Le
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Le, T. Hilbert–Schmidt Hankel Operators over Complete Reinhardt Domains. Integr. Equ. Oper. Theory 78, 515–522 (2014). https://doi.org/10.1007/s00020-013-2103-z

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  • DOI: https://doi.org/10.1007/s00020-013-2103-z

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