Bounded Toeplitz products on the Bergman space of the polydisk.
type: Item
instance of: scholarly article
title: Bounded Toeplitz products on the Bergman space of the polydisk.
zbMATH Open document ID: 1051.47025
DOI: 10.1016/S0022-247X(02)00578-4
author: Karel Stroethoff
author: Dechao Zheng
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-04T00:00:00Z
review text: Let \(L_a^2(D^n)\) be the Bergman space on the polydisk \(D^n\). The authors give a necessary and a sufficient condition for the boundedness on \(L_a^2(D^n)\) of the densely defined product of two Toeplitz operators \(T_f T_{\overline{g}}\), with \(f,g \in L_a^2(D^n)\). Both conditions are given in terms of the Berezin transform of the symbols \(f\) and \(g\).
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 32A36
Mathematics Subject Classification ID: 47B32
zbMATH DE Number: 1903476
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: Bergman space
zbMATH Keywords: polydisk
MaRDI profile type: Publication
cites work: Linear and complex analysis problem book 3. Part 1
cites work: Q4352384
cites work: Products of Hankel and Toeplitz operators on the Bergman space
cites work: The distribution function inequality and products of Toeplitz operators and Hankel operators
cites work: Q3999007
description: scientific article; zbMATH DE number 1903476