Koenigs functions, quasicircles and BMO
type: Item
instance of: scholarly article
title: Koenigs functions, quasicircles and BMO
zbMATH Open document ID: 0834.30020
DOI: 10.1215/S0012-7094-95-07813-2
author: Juha Heinonen
author: Steffen Rohde
published in: Duke Mathematical Journal
publication date: 1996-03-31T00:00:00Z
review text: An analytic function \(f\) in a hyperbolic plane domain \(\Omega\) is locally uniformly \(p\)-valent if \(f\) assumes every value at most \(p\)-times when restricted to any subset of \(\Omega\) with hyperbolic diameter at most 1. For \(\Omega= D=\) unit disk, the authors show that \(f\) is locally uniformly \(p\)-valent iff \(f\) preserves BMO. Using this they show that if \(f: D\to \mathbb{C}\) is locally uniformly \(p\)-valent and if \(f(G)\) is an univalent quasidisk image of a domain \(G\subset D\), then \(G\) itself is a quasidisk. For the quasiconformal version of this subinvariance result see [\textit{J. L. Fernández}, the first author and the reviewer, J. Anal. Math. 52, 117-132 (1989; Zbl 0677.30012)]. The last result is used to show that certain domains associated to Julia set, arising from rational approximation, and to Koenigs functions are quasidisks.
Mathematics Subject Classification ID: 30C62
Mathematics Subject Classification ID: 30C15
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 815763
zbMATH Keywords: quasicircles
zbMATH Keywords: BMO
zbMATH Keywords: Julia set
zbMATH Keywords: Koenigs functions
reviewed by: O. Martio
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 815763