Weighted differentiation composition operators to Bloch-type spaces
type: Item
instance of: scholarly article
title: Weighted differentiation composition operators to Bloch-type spaces
zbMATH Open document ID: 1331.47043
DOI: 10.1155/2013/151929
author: Junming Liu
author: Ajay K. Sharma
author: Zengjian Lou
published in: Abstract and Applied Analysis
publication date: 2014-06-20T00:00:00Z
review text: The authors provide characterizations of both the boundedness and the compactness of the weighted (iterated) differentiation composition operator \(f\mapsto \psi\cdot( f^{(n)}\circ\varphi)\), viewed from BMOA and the (usual) Bloch space to Bloch spaces with standard weights \(\alpha\) (see Theorems 5 and 7 of the paper). The key condition is the boundedness of the functions \(z\in{\mathbb D}\mapsto \displaystyle\frac{(1-|z|)^\alpha}{(1-|\varphi(z)|)^n}|\psi'(z)|\) and \(z\in{\mathbb D}\mapsto \displaystyle\frac{(1-|z|)^\alpha}{(1-|\varphi(z)|)^{n+1}}|\psi(z)\varphi'(z)| \). As often happens, the compactness characterization is obtained by replacing the boundedness condition (near the circle) with the corresponding vanishing condition.
reviewed by: Pascal Lefèvre
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 30H30
zbMATH DE Number: 6306066
zbMATH Keywords: composition operators
zbMATH Keywords: Bloch type spaces
zbMATH Keywords: BMOA
Wikidata QID: Q58915372
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/151929
OpenAlex ID: W1979604621
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description: scientific article; zbMATH DE number 6306066