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Compact composition operators acting between weighted Bergman spaces of the unit ball

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Abstract

In this paper, we study a composition operator \({C_{\varphi}}\) on the weighted Bergman space \({A_{\alpha}^p(B)}\) of the unit ball B in \({{\mathbb{C}}^N}\) . Under a natural condition we estimate the essential norm of \({C_{\varphi}}\) . As a consequence of this estimate, we also give a function-theoretic characterization of \({\varphi}\) that induces a compact composition operator on \({A_{\alpha}^p(B)}\) .

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Authors and Affiliations

  1. Faculty of Engineering, Ibaraki University, Hitachi, 316-8511, Japan

    Sei-ichiro Ueki

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  1. Sei-ichiro Ueki
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Correspondence to Sei-ichiro Ueki.

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Ueki, Si. Compact composition operators acting between weighted Bergman spaces of the unit ball. Arch. Math. 93, 461–473 (2009). https://doi.org/10.1007/s00013-009-0054-z

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  • DOI: https://doi.org/10.1007/s00013-009-0054-z

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