A Linear Composition Operator on the Bloch Space

Let n∈N0, ψ be an analytic self-map on D and u be an analytic function on D. The single operator Du,ψn acting on various spaces of analytic functions has been a subject of investigation for many years. It is defined as (Du,ψnf)(z)=u(z)f(n)(ψ(z)),f∈H(D). However, the study of the operator Pu→,ψk, whi...

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Bibliographic Details
Published inMathematics (Basel) Vol. 12; no. 15; p. 2373
Main Authors Zhu, Xiangling, Hu, Qinghua
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2024
Subjects
Analysis
Analytic functions
Bloch space
Boundary value problems
boundedness
compactness
composition operator
essential norm
Linear systems
Mathematical analysis
Operator theory
Operators (mathematics)
Tests, problems and exercises
China
Online AccessGet full text
ISSN2227-7390
2227-7390
DOI10.3390/math12152373

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Summary:Let n∈N0, ψ be an analytic self-map on D and u be an analytic function on D. The single operator Du,ψn acting on various spaces of analytic functions has been a subject of investigation for many years. It is defined as (Du,ψnf)(z)=u(z)f(n)(ψ(z)),f∈H(D). However, the study of the operator Pu→,ψk, which represents a finite sum of these operators with varying orders, remains incomplete. The boundedness, compactness and essential norm of the operator Pu→,ψk on the Bloch space are investigated in this paper, and several characterizations for these properties are provided.
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ISSN:2227-7390
2227-7390
DOI:10.3390/math12152373