Möbius invariant \(Q_p\) spaces associated with the Green's function on the unit ball of \(C^n\)
type: Item
instance of: scholarly article
title: Möbius invariant \(Q_p\) spaces associated with the Green's function on the unit ball of \(C^n\)
zbMATH Open document ID: 0893.32005
author: Caiheng Ouyang
author: Ruhan Zhao
author: Weisheng Yang
published in: Pacific Journal of Mathematics
publication date: 1997-09-16T00:00:00Z
review text: Function spaces \(Q_p(B)\) and \(Q_{p,0}(B)\), associated with the Green's function, are defined and studied for the unit ball of \(\mathbb{C}^n\). We prove that \(Q_p(B)\) and \(Q_{p,0}(B)\) are Möbius invariant Banach spaces and that \(Q_p(B)= \text{Bloch}(B)\), \(Q_{p,0}(B)= {\mathcal B}_0(B)\) (the little Bloch space) when \(1<p<n/ (n-1)\), \(Q_1=\text{BMOA} (\partial B)\) and \(Q_{1,0}(B)= \text{VMOA}(\partial B)\). This fact makes it possible for us to deal with BMOA and Bloch space in the same way. And we give necessary and sufficient conditions on boundedness (and compactness) of the Hankel operator with antiholomorphic symbols relative to \(Q_p(B)\) (and \(Q_{p,0}(B)\)). Moreover, other properties about the above spaces and \(|\varphi_z(w)|\), \(\varphi_z(w)\in \Aut(B)\), are obtained.
Mathematics Subject Classification ID: 32A37
Mathematics Subject Classification ID: 32F45
zbMATH DE Number: 1060840
zbMATH Keywords: \(Q_p\) space
zbMATH Keywords: BMOA
zbMATH Keywords: Bloch
zbMATH Keywords: Möbius invariant metric
MaRDI profile type: Publication
full work available at URL: pjm.1998.182.69
OpenAlex ID: W2122346568
DOI: 10.2140/PJM.1998.182.69
description: scientific article; zbMATH DE number 1060840