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

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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Correspondence to Xuejun Zhang.

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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).

Communicated by Tao Qian.

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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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Keywords

  • Composition operator
  • Multiplier operator
  • Boundedness
  • Compactness

Mathematics Subject Classification

  • 32A37
  • 47B33