On a Li--Stević integral-type operators between different weighted Bloch-type spaces
type: Item
instance of: scholarly article
title: On a Li--Stević integral-type operators between different weighted Bloch-type spaces
zbMATH Open document ID: 1207.47024
DOI: 10.1155/2008/780845
author: Yanyan Yu
author: Yongmin Liu
published in: Journal of Inequalities and Applications
publication date: 2009-03-30T00:00:00Z
full work available at URL: https://eudml.org/doc/117170
review text: Let \(\mathbb{D}=\left\{ z\in \mathbb{C}:\left| z\right| <1\right\} \) be the unit disk of the complex plane \(\mathbb{C}\) and let \(H(\mathbb{D})\) denote the space of all holomorphic functions on \(\mathbb{D}\). Every holomorphic self-map \(\varphi \) of the unit disc \(\mathbb{D}\) induces through composition a linear composition operator \(C_{\varphi }\) from \(H(\mathbb{D})\) to itself. The boundedness and compactness of \(C_{\varphi }\) and also of the weighted composition operator \(uC_{\varphi }\) have been well studied in various papers. \textit{S.-X.\thinspace Li} and \textit{S.\,Stević} in [J.~Math.\ Anal.\ Appl.\ 338, No.\,2, 1282--1295 (2008; Zbl 1135.47021)], for \(f,g\in H(\mathbb{D})\), defined a linear operator by \(C_{\varphi }^{g}f(z)=\int_{0}^{z}f^{\prime }(\varphi(w))g(w)\,dw\). They studied the boundedness and compactness of the operator on the Zygmund space, the Bloch-type space \(B^{\alpha },\) and the little Bloch-type space \(B_{0}^{\alpha }\). The main goal of the present paper is to characterize the boundedness and compactness of the Li-Stević integral-type operator between different weighted Bloch-type spaces.
Mathematics Subject Classification ID: 47B33
zbMATH DE Number: 5534595
Wikidata QID: Q59218068
reviewed by: Mubariz T. Karaev
MaRDI profile type: Publication
OpenAlex ID: W2033815563
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description: scientific article; zbMATH DE number 5534595