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Multiplier and Composition Operator Between Several Holomorphic Function Spaces in \(\mathbf {C^{n}}\)

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Abstract

In this paper, we characterize bounded and compact multiplier operators \(M_{u}\) on the general Hardy type spaces \(H^{p,q,s}(B_{n})\). Moreover, we also study bounded and compact composition operators \(C_{\varphi }\) from \(H^{p,q,s}(B_{n})\) to \(H^{\infty }_{\frac{q+n}{p}}(B_{n})\).

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Acknowledgements

The authors thank the reviewers and editors for their very useful suggestions!

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Authors and Affiliations

  1. College of Mathematics and Statistics, Hunan Normal University, Changsha, 410006, Hunan, China

    Si Xu & Xuejun Zhang

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  1. Si Xu
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  2. Xuejun Zhang
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Correspondence to Xuejun Zhang.

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Communicated by Tao Qian.

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This article is part of the topical collection “Higher Dimensional Geometric Function Theory and Hypercomplex Analysis” edited by Irene Sabadini, Michael Shapiro and Daniele Struppa.

The research is supported by the National Natural Science Foundation of China (No. 11571104) and the Hunan Provincial Innovation Foundation For Postgraduate (No. CX2018B286).

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Xu, S., Zhang, X. Multiplier and Composition Operator Between Several Holomorphic Function Spaces in \(\mathbf {C^{n}}\). Complex Anal. Oper. Theory 15, 36 (2021). https://doi.org/10.1007/s11785-021-01081-y

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