The multiplication operator from mixed-norm to \(n\)-th weighted-type spaces on the unit disk
type: Item
instance of: scholarly article
zbMATH Open document ID: 1315.47032
author: Yongmin Liu
author: Yanyan Yu
publication date: 2012-05-23T00:00:00Z
Mathematics Subject Classification ID: 47B38
Mathematics Subject Classification ID: 47B33
Mathematics Subject Classification ID: 30H05
Mathematics Subject Classification ID: 30D45
Mathematics Subject Classification ID: 46E15
zbMATH DE Number: 6037650
zbMATH Keywords: multiplication operator
zbMATH Keywords: mixed-norm space
zbMATH Keywords: \(n\)th weighted-type spaces
MaRDI profile type: Publication
full work available at URL: mia-15-38
OpenAlex ID: W2328397942
DOI: 10.7153/MIA-15-38
title: The multiplication operator from mixed-norm to \(n\)-th weighted-type spaces on the unit disk
published in: Mathematical Inequalities \& Applications
review text: The \(n\)th weighted-type spaces on the unit disk \(\mathbb D\) consist of all \(u \in H(\mathbb D)\) such that NEWLINE\[NEWLINEb(f)=\sup_{z\in \mathbb D}\mu(z)|f^{(n)}(z)|<\infty,NEWLINE\]NEWLINE where \(\mu(z)\) is a positive continuous function on \(\mathbb D\) such that \(\mu(z)=\mu(|z|)\). The multiplication operator \(M_{\Phi}\) is defined by \(M_{\Phi}f=\Phi f\). In the present paper, the authors obtain basic results on the boundedness and compactness of the multiplication operator from mixed-norm spaces to \(n\)th weighted-type spaces on the unit disk. The paper is written very carefully and nicely. The terms used in the paper have also been explained in detail.
reviewed by: Mubariz T. Karaev
description: scientific article; zbMATH DE number 6037650