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Stević-Sharma Operator on Spaces of Vector-Valued Holomorphic Functions

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Abstract

In this paper, we are interested in the Stević-Sharma operator on the spaces of vector-valued holomorphic functions, which has never been considered so far. We completely characterize the boundedness of the Stević-Sharma operator between weak and strong vector-valued Bergman spaces in terms of a Julia-Carathéodory type function theoretic characterization and a power type characterization. Furthermore, we establish an interesting result: the boundedness of the Stević-Sharma operator between weak and strong vector-valued Bergman spaces is not only equivalent to the Hilbert-Schmidtness but also equivalent to the order boundedness of the Stević-Sharma operator between scalar value Bergman spaces.

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Acknowledgements

The authors are sincerely grateful to the anonymous referees for their careful reading of the initial version of the manuscript and helpful suggestions. X. Guo was supported by China Postdoctoral Science Foundation (2020M672399) and National Natural Science Foundation of China (12101467).

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Authors and Affiliations

  1. School of Mathematics and Statistics, **nyang Normal University, **nyang, 464000, China

    Zeng Fan

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

    **n Guo

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  1. Zeng Fan
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  2. **n Guo
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Correspondence to **n Guo.

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Communicated by Dan Volok.

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Fan, Z., Guo, X. Stević-Sharma Operator on Spaces of Vector-Valued Holomorphic Functions. Complex Anal. Oper. Theory 16, 80 (2022). https://doi.org/10.1007/s11785-022-01255-2

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  • DOI: https://doi.org/10.1007/s11785-022-01255-2

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