Weighted spaces of holomorphic functions on balanced domains
type: Item
instance of: scholarly article
title: Weighted spaces of holomorphic functions on balanced domains
zbMATH Open document ID: 0803.46023
author: José Bonet
author: Antonio Galbis
author: Klaus Dieter Bierstedt
published in: Michigan Mathematical Journal
publication date: 1995-01-02T00:00:00Z
review text: This paper deals with radial weights on balanced domains \(G\subset \mathbb{C}^ n\), for which it is possible to apply methods involving the Taylor series of holomorphic functions about zero. The contractive properties of the Cesàro means of the Taylor series of functions in the disk algebra are used to derive remarkable consequences for spaces of holomorphic functions on arbitrary balanced open sets in \(\mathbb{C}^ n\). This leads to simple proofs that the spaces \(HV_ 0(G)\) and \({\mathcal V}_ 0 H(G)\) have the bounded approximation property whenever they contain the polynomials, and that then the polynomials are dense. The second part of the paper is devoted to a related problem on \(\varepsilon\)-tensor products with an arbitrary Banach space with applications to certain spaces of vector-valued holomorphic functions. In the last part some remarkable vector-valued generalizations of the (bi- )dualities \(((HV_ 0(G)_ b')_ b'= HV(G)\) and \((({\mathcal V}_ 0 H(G))_ b')_ i'= {\mathcal V} H(G)\) are established.
Mathematics Subject Classification ID: 46E10
Mathematics Subject Classification ID: 32A07
Mathematics Subject Classification ID: 46B28
Mathematics Subject Classification ID: 46M05
zbMATH DE Number: 474971
zbMATH Keywords: radial weights on balanced domains
zbMATH Keywords: contractive properties of the Cesàro means of the Taylor series of functions in the disk algebra
zbMATH Keywords: spaces of holomorphic functions
zbMATH Keywords: bounded approximation property
zbMATH Keywords: \(\varepsilon\)-tensor products
zbMATH Keywords: spaces of vector-valued holomorphic functions
reviewed by: Fritz Haslinger
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1307/mmj/1029004753
OpenAlex ID: W2075803991
DOI: 10.1307/MMJ/1029004753
description: scientific article; zbMATH DE number 474971