Weighted composition operators from the Bloch space and the analytic Besov spaces into the Zygmund space
type: Item
instance of: scholarly article
title: Weighted composition operators from the Bloch space and the analytic Besov spaces into the Zygmund space
zbMATH Open document ID: 1323.47026
DOI: 10.1155/2013/154029
author: Flavia Colonna
author: Songxiao Li
published in: Journal of Operators
publication date: 2014-11-19T00:00:00Z
review text: Summary: We provide several characterizations of the bounded and the compact weighted composition operators from the Bloch space \(\mathbb B\) and the analytic Besov spaces \(B_p\) (with \(1 < p < \infty\)) into the Zygmund space \(\mathcal Z\). As a special case, we show that the bounded (resp., compact) composition operators from \(\mathcal B\), \(B_p\), and \(H^{\infty}\) to \(\mathcal Z\) coincide. In addition, the boundedness and the compactness of the composition operator can be characterized in terms of the boundedness (resp., convergence to 0, under the boundedness assumption of the operator) of the Zygmund norm of the powers of the symbol.
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 30H30
zbMATH DE Number: 6371121
zbMATH Keywords: boundedness
zbMATH Keywords: compactness
zbMATH Keywords: composition operator
Wikidata QID: Q59020394
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/154029
OpenAlex ID: W2163616812
cites work: Composition operators on some Möbius invariant Banach spaces
cites work: Analytic Besov spaces
cites work: Q5618011
cites work: Q4888816
cites work: Composition operators and classical function theory
cites work: The Isometries of Some Function Spaces
cites work: The Isometries of Hp
cites work: Isometries of Weighted Bergman Spaces
cites work: Isometries of the Disc Algebra
cites work: Generalized composition operators on Zygmund spaces and Bloch type spaces
cites work: Weighted composition operators from Zygmund spaces into Bloch spaces
cites work: Weighted composition operators from the Besov spaces into the Bloch spaces
cites work: Compact composition operators on BMOA and the Bloch space
cites work: New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space
cites work: Weighted composition operators from the minimal Möbius invariant space into the Bloch space
cites work: WEIGHTED COMPOSITION OPERATORS BETWEEN H∞AND BMOA
description: scientific article; zbMATH DE number 6371121