On a criterion for continuity and compactness of composition operators on the weighted Bloch space
type: Item
instance of: scholarly article
title: On a criterion for continuity and compactness of composition operators on the weighted Bloch space
zbMATH Open document ID: 1333.30069
author: René Erlín Castillo
author: Carlos E. Marrero-Rodríguez
author: Julio C. Ramos Fernández
published in: Mediterranean Journal of Mathematics
publication date: 2015-09-03T00:00:00Z
review text: The authors deal with the weighted Bloch space \(B^{\mathrm{log}}\) of all holomorphic functions on the complex unit disc \(\mathbb{D}\) satisfying the growth condition \[ \sup_{z\in \mathbb{D}} (1-|z|^2) \log\left( \frac{e}{(1-|z|^2)} \right) |f'(z)| < +\infty , \] and characterize the continuity and compactness of the composition operators \( \mathcal{C}_\psi(f) := f \circ \psi \) acting on \(B^{\mathrm{log}}\), for given holomorphic self-maps \(\psi\) of \(\mathbb{D}\). The characterization is given in terms of the quantity \({\left\| \sigma_a \circ \psi \right\|}\), where \(\sigma_a \), \(1/2 < |a| < 1\), is a specific class of functions on \(\mathbb{D}\).
reviewed by: Allal Ghanmi
Mathematics Subject Classification ID: 30H30
Mathematics Subject Classification ID: 47B33
zbMATH DE Number: 6478193
zbMATH Keywords: weighted Bloch spaces
zbMATH Keywords: composition operators
MaRDI profile type: Publication
full work available at URL: s00009-014-0427-9
OpenAlex ID: W2056006417
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DOI: 10.1007/S00009-014-0427-9
description: scientific article; zbMATH DE number 6478193