Trace ideal criteria for Toeplitz and Hankel operators on the weighted Bergman spaces with exponential type weights
type: Item
instance of: scholarly article
title: Trace ideal criteria for Toeplitz and Hankel operators on the weighted Bergman spaces with exponential type weights
zbMATH Open document ID: 0853.47015
author: Peng Lin
author: Richard Rochberg
published in: Pacific Journal of Mathematics
publication date: 1996-07-28T00:00:00Z
review text: Let \(\varphi: \mathbb{D}\to \mathbb{R}\) be a subharmonic function and let \(AL^2_\varphi(\mathbb{D})\) denote the closed subspace of \(L^2(\mathbb{D}, e^{- 2\varphi} dA)\) consisting of analytic functions in the unit disk \(\mathbb{D}\). For a certain class of subharmonic \(\varphi\), the necessary and sufficient conditions are obtained for the Toeplitz operator \(T_\mu\) on \(AL^2_\varphi(\mathbb{D})\) and the Hankel operator \(H_b\) on \(AL^2_\varphi(\mathbb{D})\) in order that they belong to the Schatten-von Neumann class \(S_p\).
reviewed by: Ke-Pao Lin
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 46J15
zbMATH DE Number: 910280
zbMATH Keywords: subharmonic function
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: Hankel operator
zbMATH Keywords: Schatten-von Neumann class
MaRDI profile type: Publication
full work available at URL: pjm.1996.173.127
OpenAlex ID: W1531772299
DOI: 10.2140/PJM.1996.173.127
description: scientific article; zbMATH DE number 910280