Composition operator on Bers-type spaces.
type: Item
instance of: scholarly article
title: Composition operator on Bers-type spaces.
zbMATH Open document ID: 1043.47023
DOI: 10.1016/S0252-9602(17)30310-7
author: Weixiang He
author: L. Jiang
published in: Acta Mathematica Scientia. Series B. (English Edition)
publication date: 2002-01-01T00:00:00Z
review text: Let \(D\) be the unit disk and let \(A(D)\) denote the set of analytic functions on \(D\). For \(\alpha\in (0,\infty)\), let \[ \begin{aligned} H^\infty_\alpha &= \Biggl\{f\in A(D)\,\biggl|\, \sup_{z\in D} (1-| z|)^\alpha| f(z)|< \infty\Biggr\},\\ H^\infty_{\alpha,0} &= \Biggl\{f\in A(D)\,\biggl|\, \lim_{| z|\to 1}(1- | z|)^\alpha| f(z)|= 0\Biggr\},\end{aligned} \] \(H^\infty_\alpha\) (or \(H^\infty_{\alpha,0}\)) is called Bers-type space. The goal of the paper under review is to give necessary and sufficient conditions for a composition operator to be bounded or compact on \(H^\infty_\alpha\) and \(H^\infty_{\alpha,0}\).
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 30D45
Mathematics Subject Classification ID: 46E15
Mathematics Subject Classification ID: 47B07
zbMATH DE Number: 1824211
zbMATH Keywords: Bers-type space
zbMATH Keywords: composition operator
zbMATH Keywords: boundedness
zbMATH Keywords: compactness
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: s0252-9602(17)30310-7
OpenAlex ID: W2783250970
description: scientific article; zbMATH DE number 1824211