Holomorphic functions, measures and BMO
type: Item
instance of: scholarly article
title: Holomorphic functions, measures and BMO
zbMATH Open document ID: 0609.30034
DOI: 10.1007/BF02384401
published in: Arkiv för Matematik
publication date: 1986-01-01T00:00:00Z
review text: Let M denote the finite strictly positive measures on the cirlce \({\mathbb{T}}\). The author proves that for \(| z_ 0| <1\), f in the disc algebra and \(f(z_ 0)\not\in f(T)\) then for every \(\mu\) in M there is an interval \(I\subset T\) such that \[ f(z_ 0)=\frac{1}{\mu (I)}\int_{I}fd\mu. \] The proof involves a study of winding numbers. He gives examples to prove that some of the hypothesis can not be weakened.
Mathematics Subject Classification ID: 30D55
zbMATH DE Number: 3985589
zbMATH Keywords: finite measure
zbMATH Keywords: Blaschke product
zbMATH Keywords: winding numbers
author: V. Nestoridis
MaRDI profile type: Publication
cites work: Q5618011
cites work: \(H^p\) spaces of several variables
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full work available at URL: https://doi.org/10.1007/bf02384401
OpenAlex ID: W2015105901
description: scientific article; zbMATH DE number 3985589