Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space
type: Item
instance of: scholarly article
title: Algebraic properties of Toeplitz and small Hankel operators on the harmonic Bergman space
zbMATH Open document ID: 1314.47044
author: Hongyan Guan
author: Yufeng Lu
publication date: 2014-09-11T00:00:00Z
review text: The harmonic Bergman space \(L^2_{\mathrm{h}}\) is, by definition, the subspace of the space \(L^2\) with respect to area measure on the unit disc that consists of harmonic functions. Let \(Q\) be the orthogonal projection onto \(L^2_{\mathrm{h}}\). Given a bounded function \(\varphi\) on the unit disk, the Toeplitz operator \(T_\varphi\) and the Hankel operator \(H_\varphi\) are defined by \[ T_\varphi f=Q(\varphi f)\quad\text{and}\quad H_\varphi f=QU(\varphi f), \] where \((Uf)(z)=f(\bar z)\). The authors of the paper under review discuss algebraic properties of Toeplitz and Hankel operators.
reviewed by: Vladimir V. Peller
Mathematics Subject Classification ID: 47B35
zbMATH DE Number: 6342510
zbMATH Keywords: Toeplitz operator
zbMATH Keywords: small Hankel operator
zbMATH Keywords: quasihomogeneous symbols
zbMATH Keywords: harmonic Bergman space
zbMATH Keywords: Mellin transform
MaRDI profile type: Publication
full work available at URL: s10114-014-3276-3
OpenAlex ID: W2143721708
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DOI: 10.1007/S10114-014-3276-3
published in: Acta Mathematica Sinica, English Series
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description: scientific article; zbMATH DE number 6342510