On higher dimensional Luecking's theorem
type: Item
instance of: scholarly article
title: On higher dimensional Luecking's theorem
zbMATH Open document ID: 1162.47027
author: Boo Rim Choe
published in: Journal of the Mathematical Society of Japan
publication date: 2009-03-20T00:00:00Z
review text: Let \(\Omega\) be a complete circular domain in \(\mathbb{C}^n\), and let \(\mu\) be a complex Borel measure on \(\Omega\). The main result of the paper states that the Toeplitz operator \(T_{\mu}\) acting on the Bergman space of analytic (or pluriharmonic) functions in \(\Omega\) has a finite rank if and only if \(\mu\) is a linear combination of point masses. This result provides to a higher-dimensional extension of a result of \textit{D.\,H.\thinspace Luecking} [Proc.\ Am.\ Math.\ Soc.\ 136, No.\,5, 1717--1723 (2008; Zbl 1152.47021)].
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 46E20
Mathematics Subject Classification ID: 32A36
zbMATH DE Number: 5530296
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: Bergman space
zbMATH Keywords: finite rank
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2969/jmsj/06110213
OpenAlex ID: W2079681617
cites work: Berezin transforms on pluriharmonic Bergman spaces
cites work: Trace ideal criteria for Toeplitz operators
cites work: Finite rank Toeplitz operators on the Bergman space
cites work: Q4340096
DOI: 10.2969/JMSJ/06110213
description: scientific article; zbMATH DE number 5530296