Counting functions and majorization for Jensen measures
type: Item
instance of: scholarly article
title: Counting functions and majorization for Jensen measures
zbMATH Open document ID: 0566.32011
published in: Pacific Journal of Mathematics
publication date: 1986-01-01T00:00:00Z
review text: We establish for uniform algebras a generalization of the classical identities of Hardy and Stein. We use this and an estimate based on the isoperimetric inequality to give a proof of H. Alexander's spectral area theorem. We use similar methods to prove a slight generalization of the following result of \textit{S. Axler} and \textit{J. H. Shapiro} [Math. Ann. 271, 161-183 (1985; Zbl 0541.30041)]: if f is a bounded holomorphic function on the unit ball in \({\mathbb{C}}^ n\) and the cluster set at each point in the boundary of the ball has zero area then f belongs to VMOA.
Mathematics Subject Classification ID: 32E35
Mathematics Subject Classification ID: 32A07
zbMATH DE Number: 3903027
zbMATH Keywords: spectral area theorem
zbMATH Keywords: bounded holomorphic function on the unit ball
zbMATH Keywords: VMOA
author: Charles S. Stanton
MaRDI profile type: Publication
full work available at URL: pjm.1986.125.459
OpenAlex ID: W2010895840
DOI: 10.2140/PJM.1986.125.459
description: scientific article; zbMATH DE number 3903027