\(BMO\) and Hankel operators on Bergman spaces
type: Item
instance of: scholarly article
title: \(BMO\) and Hankel operators on Bergman spaces
zbMATH Open document ID: 0771.32007
author: Kehe Zhu
published in: Pacific Journal of Mathematics
publication date: 1993-05-16T00:00:00Z
review text: Let \(\text{BMO}_ \partial^ p\) be the space of functions on the open unit ball in \(\mathbb{C}^ n\) with bounded mean oscillation in the Bergman metric defined using the volume \(L^ p\) integral. Here the author studies the structure of \(\text{BMO}_ \partial^ p\), in particular how \(\text{BMO}_ \partial^ p\) depends on \(p\). He also characterizes \(\text{BMO}_ \partial^ p\) in terms of certain Hankel operators acting on weighted Bergman \(L^ p\) spaces. Further, the author studies in parallel the companion space \(\text{VMO}_ \partial^ p\) which is the subspace of \(\text{BMO}_ \partial^ p\) generated by functions in \(C(\overline B_ n)\) and functions with compact support.
Mathematics Subject Classification ID: 32A37
zbMATH DE Number: 165402
zbMATH Keywords: BMO
zbMATH Keywords: VMO
zbMATH Keywords: bounded mean oscillation
zbMATH Keywords: Hankel operators
reviewed by: Arun Kumar Agarwal
MaRDI profile type: Publication
full work available at URL: pjm.1992.155.377
OpenAlex ID: W1999281468
DOI: 10.2140/PJM.1992.155.377
description: scientific article; zbMATH DE number 165402