Bounded Toeplitz products on the weighted Bergman spaces of the unit ball
type: Item
instance of: scholarly article
title: Bounded Toeplitz products on the weighted Bergman spaces of the unit ball
zbMATH Open document ID: 1186.47026
author: Jie Miao
published in: Journal of Mathematical Analysis and Applications
publication date: 2008-07-21T00:00:00Z
review text: The author considers special products of Toeplitz operators of the form \(T_f T_{\overline{g}}\) on the weighted Bergman space \(A_{\alpha}^p\) of the unit ball in \(\mathbb{C}^n\), where \(1\leq p<\infty\), \(\alpha>-1\). Recently, \textit{K.\,Stroethoff} and \textit{D.\,C.\thinspace Zheng} [J.~Math.\ Anal.\ Appl.\ 325, No.\,1, 114--129 (2007; Zbl 1111.32003)] have studied the boundedness and invertibility of such products on the space \(A_{\alpha}^2\) of the ball. In the paper under review, the author extends their results. Also, a different approach is used, which is based on reproducing kernels.
reviewed by: Dragan Vukotić
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 32A36
zbMATH DE Number: 5303215
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: weighted Bergman space of the unit ball
zbMATH Keywords: reproducing kernel
zbMATH Keywords: bounded operator
MaRDI profile type: Publication
full work available at URL: j.jmaa.2008.05.078
OpenAlex ID: W2002513477
cites work: Bounded Toeplitz products on the Bergman space of the unit ball in \(\mathbb C^n\)
cites work: Products of Hankel and Toeplitz operators on the Bergman space
cites work: Bounded Toeplitz products on the Bergman space of the polydisk.
cites work: Bounded Toeplitz products on Bergman spaces of the unit ball
cites work: Q3523863
cites work: Bergman and Hardy spaces with small exponents
cites work: Spaces of Holomorphic Functions in the Unit Ball
DOI: 10.1016/J.JMAA.2008.05.078
description: scientific article; zbMATH DE number 5303215