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Weighted Composition-differentiation Operators on the Bergman Space

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Abstract

In this paper, we study weighted composition-differentiation operators of the form \(D_{n,\varphi , \psi }\) on the Bergman space \(A^{2}\). We obtain explicit conditions for \(D_{n,\varphi , \psi }\) when it is complex symmetric with respect to conjugations \({\mathcal {C}}_{1}\) and \({\mathcal {C}}_{2}\) respectively. In addition, invariant subspaces of composition-differentiation operators are considered. Finally, we give spectral properties of weighted composition-differentiation operators.

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Acknowledgements

The authors wish to thank the referee for a careful reading and valuable comments for the original draft.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang, 050061, China

    Kaikai Han

  2. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Maofa Wang

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  1. Kaikai Han
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  2. Maofa Wang
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Correspondence to Kaikai Han.

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Communicated by Bernd Kirstein.

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This work was partially supported by NSFC (11771340).

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Han, K., Wang, M. Weighted Composition-differentiation Operators on the Bergman Space . Complex Anal. Oper. Theory 15, 89 (2021). https://doi.org/10.1007/s11785-021-01116-4

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  • DOI: https://doi.org/10.1007/s11785-021-01116-4

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