New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space
type: Item
instance of: scholarly article
title: New criteria for boundedness and compactness of weighted composition operators mapping into the Bloch space
zbMATH Open document ID: 1279.47041
author: Flavia Colonna
published in: Central European Journal of Mathematics
publication date: 2013-01-30T00:00:00Z
review text: For Banach spaces of analytic functions \(X\) and \(Y\) over a domain \(\Omega\subset\mathbb{C}\) with \(\psi\) analytic on \(\Omega\) and \(\phi\) an analytic self-map of \(\Omega\), the weighted composition operator with symbols \(\psi\) and \(\phi\) from \(X\) to \(Y\) is the operator \(W_{\psi,\phi} f=M_\psi C_\phi f=\psi(f\circ\phi)\). In the paper under review, for \(\Omega=\mathbb{D}\), the author studies the bounded and compact weighted composition operators from the Hardy space \(H^p\), the Bloch space, the weighted Bergman spaces, and the Dirichlet space into the Bloch space in terms of the Bloch norms of \(W_{\psi,\phi} f\) for suitable functions \(f\).
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 30H30
Mathematics Subject Classification ID: 30H10
Mathematics Subject Classification ID: 30H20
zbMATH DE Number: 6132914
zbMATH Keywords: weighted composition operators
zbMATH Keywords: Bloch space
zbMATH Keywords: Hardy space
zbMATH Keywords: weighted Bergman space
zbMATH Keywords: Dirichlet space
reviewed by: Brett Wick
MaRDI profile type: Publication
full work available at URL: s11533-012-0097-4
OpenAlex ID: W2147031041
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DOI: 10.2478/S11533-012-0097-4
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description: scientific article; zbMATH DE number 6132914