Weighted composition operators between different weighted Bergman spaces in polydiscs
type: Item
instance of: scholarly article
title: Weighted composition operators between different weighted Bergman spaces in polydiscs
zbMATH Open document ID: 1123.47023
author: Songxiao Li
published in: Vietnam Journal of Mathematics
publication date: 2007-05-14T00:00:00Z
review text: Let \(D^n\) be the unit polydisc in \({\mathbb C}^n\), \(n\in{\mathbb N}\). For \(1<p<\infty\) and \(\alpha>-1\), let \(A_\alpha^p(D^n)\) be the usual weighted Bergman spaces, the weight being \(z\mapsto\prod_{k=1}^n(1-| z_k| ^2)^\alpha\). Let \(\phi:D^n\to D^n\) and \(\psi:D^n\to{\mathbb C}\) be holomorphic. The author characterizes when, for \(\alpha,\beta>-1\), \(\eta\geq 1\) and \(1<p<\infty\), the weighted composition operator \(f\mapsto\psi(\cdot)\cdot f(\phi(\cdot))\) defines a bounded (resp., compact) operator \(A_\alpha^p(D^n)\to A_\beta^{\eta p}(D^n)\). The characterizations are in terms of properties of suitable Carleson measures on \(\overline{D^n}\).
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 32A36
zbMATH DE Number: 5152632
zbMATH Keywords: weighted Bergman spaces on polydiscs
zbMATH Keywords: weighted composition operators
zbMATH Keywords: Carleson measures
reviewed by: Hans Jarchow
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5152632