Generalized multiplication operators on weighted Hardy spaces
type: Item
instance of: scholarly article
title: Generalized multiplication operators on weighted Hardy spaces
zbMATH Open document ID: 1285.47037
DOI: 10.1134/S1995080211040226
author: Sunil K. Sharma
author: B. S. Komal
published in: Lobachevskii Journal of Mathematics
publication date: 2012-12-12T00:00:00Z
review text: The authors consider operators \(M^d_\theta f= \theta f'\) for functions \(\theta\) and \(f\) holomorphic in \(\Omega\) and call them ``generalized multiplication'' operators. The paper contains some facts about the action of such operators on what the authors idiosyncratically call ``weighted Hardy spaces'' \(H^p(\beta)\) given by holomorphic functions \(f=\sum_{n}f_n z^n\) with \(\sum_n |f_n|^p\beta_n<\infty\). Then some conditions on the weights for boundedness and compactness are provided. It is also shown that the only case of Hermitian operators occurs whenever \(\theta(z)=az\) for a real number \(a\).
reviewed by: Oscar Blasco
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 6115190
zbMATH Keywords: generalized multiplication operator
zbMATH Keywords: compact operator
zbMATH Keywords: normal operator
zbMATH Keywords: Hermitian operator
zbMATH Keywords: adjoint of an operator
MaRDI profile type: Publication
cites work: Hermitian weighted composition operators and Bergman extremal functions
cites work: Q4888816
cites work: Compact weighted composition operators on the Hardy space
cites work: Multiplication operators and composition operators with closed ranges
cites work: Composition operators
cites work: Q4059478
cites work: Cyclic composition operators on smooth weighted Hardy spaces
description: scientific article; zbMATH DE number 6115190