Weighted Composition Operators from H∞ to α,m-Bloch Space on Cartan-Hartogs Domain of the First Type

Let YI be nonhomogeneous Cartan-Hartogs domain of the first type, ϕ a holomorphic self-map, and ψ a fixed holomorphic function on YI. We study the weighted composition operator ψCϕf=ψf∘ϕ for a function f holomorphic on YI. Our main results generalize both cases of the unit ploydisc and the unit ball...

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Bibliographic Details
Published in:Journal of function spaces Vol. 2022; pp. 1 - 13
Main Authors: Su, Jianbing, Zhang, Ziyi
Format: Journal Article
Language:English
Published: New York Hindawi 2022
John Wiley & Sons, Inc
Wiley
Subjects:
Analytic functions
Banach spaces
Composition
Domains
H infinity
Mathematical analysis
Operators (mathematics)
ISSN:2314-8896, 2314-8888
Online Access:Get full text
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Summary:Let YI be nonhomogeneous Cartan-Hartogs domain of the first type, ϕ a holomorphic self-map, and ψ a fixed holomorphic function on YI. We study the weighted composition operator ψCϕf=ψf∘ϕ for a function f holomorphic on YI. Our main results generalize both cases of the unit ploydisc and the unit ball obtained by Li and Stević (Li 2007 and Li 2008). Firstly, we obtain two crucial inequalities on YI; furthermore, the boundedness and compactness of operator ψCϕ from the space H∞ of all bounded holomorphic functions to the α,m-Bloch space Bα,m on YI are investigated.
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ISSN:2314-8896
2314-8888
DOI:10.1155/2022/4732049