Properties of Toeplitz operators on some holomorphic Banach function spaces
type: Item
instance of: scholarly article
title: Properties of Toeplitz operators on some holomorphic Banach function spaces
zbMATH Open document ID: 1263.47031
DOI: 10.1155/2012/517689
author: A. El-Sayed Ahmed
author: Mahmoud Ali Bakhit
published in: Journal of Function Spaces and Applications
publication date: 2012-08-03T00:00:00Z
reviewed by: Vladimir S. Pilidi
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 30H20
Mathematics Subject Classification ID: 30H25
zbMATH DE Number: 6063096
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: Besov space
zbMATH Keywords: boundedness
zbMATH Keywords: compactness
Wikidata QID: Q58908291
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/517689
OpenAlex ID: W2098329009
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review text: For \(\alpha>-1\) and a positive Borel measure \(\mu\) on the unit ball \({\mathbb B}_{n}\subset {\mathbb C}_{n}\) such that NEWLINE\[NEWLINE \left| \int_{{\mathbb B}_{n}} (1-|w|^{\alpha}) \,d\mu(w) \right| <\infty, NEWLINE\]NEWLINE the associated Toeplitz operator is defined by the formula NEWLINE\[NEWLINE (T_{\mu}^{\alpha}f)(z) = c_{\alpha} \int_{{\mathbb B}_{n}} \frac{(1-|w|^{2})^{\alpha}f(w)}{(1-\langle z,w \rangle)^{n+\alpha+1}} \, d\mu(w), NEWLINE\]NEWLINE where \(w\in{\mathbb B}_{n}\), \(\langle \cdot,\cdot \rangle\) is the scalar product in \({\mathbb C}_{n}\), \(c_{\alpha}\) is the normalizing constant.NEWLINENEWLINEUnder some additional assumptions, the authors characterize those measures for which these operators are bounded or compact on some spaces of holomorphic functions on \({\mathbb B}_{n}\), including the case of Besov spaces.
description: scientific article; zbMATH DE number 6063096