Toeplitz operators and weighted norm inequalities on the bidisc
type: Item
instance of: scholarly article
zbMATH Open document ID: 0993.47027
author: Takahiko Nakazi
publication date: 2002-09-16T00:00:00Z
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 42B20
zbMATH DE Number: 1654988
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: weighted norm inequality
zbMATH Keywords: several variables
zbMATH Keywords: invertibility
zbMATH Keywords: Hankel operator
zbMATH Keywords: Lebesgue space
zbMATH Keywords: Hardy space on the bidisc
zbMATH Keywords: invertibility problem
zbMATH Keywords: weighted norm inequalities
MaRDI profile type: Publication
full work available at URL: mia-04-38
OpenAlex ID: W2751223542
DOI: 10.7153/MIA-04-38
title: Toeplitz operators and weighted norm inequalities on the bidisc
published in: Mathematical Inequalities \& Applications
review text: Let \(m\) be the normalized Lebesgue measure on the torus \(T^2\) and let \(L^p=L^p(T^2, m),1\leq p \leq \infty\), denote the Lebesgue space on \(T^2\), and let \(H^p=H^p(T^2, m)=\{f\in L^p, \widehat{f} (\ell, n)=0\) if \(\ell<0\) or \(n<0\}\), \(1<p<\infty\), be the Hardy space on the bidisc respectively. The author studies the Hankel \(H_\varphi\) and Toeplitz \(T_\varphi\) operators on \(H^p\) with \(\varphi\in H^\infty\). He gives two-sided estimates for norm of \(H_\varphi\) and considers the invertibility problem for \(T_\varphi\) using the weighted norm inequalities.
reviewed by: N. Karapetiants
description: scientific article; zbMATH DE number 1654988