Boundedness and compactness of generalized Hankel operators on bounded symmetric domains
type: Item
instance of: scholarly article
title: Boundedness and compactness of generalized Hankel operators on bounded symmetric domains
zbMATH Open document ID: 0880.47015
published in: Journal of Functional Analysis
publication date: 1998-02-08T00:00:00Z
review text: Let \(D\) be a domain in \(\mathbb{C}^n\), the Hankel operator associated with an analytic function \(b\) on \(D\) is \(H_b=(I-P)M_{\overline b}P\), where \(M_{\overline b}\) is the multiplication by \(\overline b\), and \(P\) is a projection. In this paper, when \(D\) is a Cartan domain of tube type, of dimension \(n\), and of rank \(r>1\), in \(\mathbb{C}^n\), the author introduces the generalization \(A_b\) of the Hankel operator \(H_b\), the generalized Bloch and little Bloch spaces \(B\), \(B_0\), and the generalized invariant oscillation spaces BMOA, VMOA. Main results of the author: \(A_b\) is bounded if and only if \(b\in B\) if and only if \(b\in\text{BMOA}\). \(A_b\) is compact if and only if \(b\in B_0\) if and only if \(b\in\text{VMOA}\). \(A_b\) belongs to the Hilbert-Schmidt class \(S_2\) if and only if \(b\) is in the generalized Besov space \(B_2\).
Mathematics Subject Classification ID: 47B35
Mathematics Subject Classification ID: 47B10
Mathematics Subject Classification ID: 47B07
zbMATH DE Number: 871731
zbMATH Keywords: compactness
zbMATH Keywords: Hankel operator
zbMATH Keywords: multiplication
zbMATH Keywords: projection
zbMATH Keywords: Cartan domain of tube type
zbMATH Keywords: generalized Bloch and little Bloch spaces
zbMATH Keywords: generalized invariant oscillation spaces
zbMATH Keywords: Hilbert-Schmidt class
zbMATH Keywords: generalized Besov space
author: Jonathan Arazy
MaRDI profile type: Publication
OpenAlex ID: W2042988803
DOI: 10.1006/JFAN.1996.0042
description: scientific article; zbMATH DE number 871731