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Composition Operators of Bloch-Type Spaces on Bounded Symmetric Domains

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Abstract

Let \({\mathbb {B}}_X\) be a bounded symmetric domain realized as the open unit ball \({\mathbb {B}}_X\) of a finite dimensional JB*-triple X. In this paper, we continue the work related to the composition operator \(C_{\varphi }\) between Bloch-type spaces, where \(\varphi \) is a holomorphic mapping from \({\mathbb {B}}_X\) into the unit polydisc \({\mathbb {U}}^n\) in \({\mathbb {C}}^n\). We first give a necessary and sufficient condition for the composition operator from the \(\alpha \)-Bloch space into the \(\beta \)-Bloch space to be bounded. Next, we give a necessary condition for \(C_{\varphi }\) to be compact.

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Correspondence to Hidetaka Hamada.

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Communicated by Heinrich Begehr.

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Tatsuhiro Honda was partially supported by JSPS KAKENHI Grant Number JP20K03640.

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.

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Hamada, H., Honda, T. Composition Operators of Bloch-Type Spaces on Bounded Symmetric Domains. Complex Anal. Oper. Theory 16, 6 (2022). https://doi.org/10.1007/s11785-021-01182-8

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