A Linear Composition Operator on the Bloch Space

Xiangling Zhu () and Qinghua Hu
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Xiangling Zhu: University of Electronic Science and Technology of China, Zhongshan Institute, Zhongshan 528402, China
Qinghua Hu: School of Mathematical Sciences, Qufu Normal University, Qufu 273100, China

Mathematics, 2024, vol. 12, issue 15, 1-17

Abstract: Let n ∈ N 0 , ψ be an analytic self-map on D and u be an analytic function on D . The single operator D u , ψ n acting on various spaces of analytic functions has been a subject of investigation for many years. It is defined as ( D u , ψ n f ) ( z ) = u ( z ) f ( n ) ( ψ ( z ) ) , f ∈ H ( D ) . However, the study of the operator P u → , ψ k , which represents a finite sum of these operators with varying orders, remains incomplete. The boundedness, compactness and essential norm of the operator P u → , ψ k on the Bloch space are investigated in this paper, and several characterizations for these properties are provided.

Keywords: Bloch space; composition operator; boundedness; compactness; essential norm (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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