Universal Teichmüller space and BMO
type: Item
instance of: scholarly article
title: Universal Teichmüller space and BMO
zbMATH Open document ID: 1269.30030
author: Huaying Wei
author: Yuliang Shen
published in: Advances in Mathematics
publication date: 2013-02-11T00:00:00Z
review text: In the BMO theory of the universal Teichmüller space, some characterizations of the BMOA-Teichmüller space are well known. The authors give two more equivalent characterizations by using some kernel functions and corresponding operators induced by quasisymmetric homeomorphisms. Various equivalent characterizations of the VMOA-Teichmüller space are also given in this paper. The authors also prove that BMO-Teichmüller spaces have natural complex structures in different models, and this is applied to prove that if a homeomorphism \(h\) of \(S^1\) is absolutely continuous with \(\log h'\) belonging to \(\mathrm{VMO}(S^1)\), then \(\log f'\) belongs to \(\mathrm{VMOA}(\triangle)\), where \(f\) is a bounded conformal mapping on \(\triangle\) and \(h\) is the corresponding quasisymmetric conformal welding.
reviewed by: Chong Wu
Mathematics Subject Classification ID: 30C62
Mathematics Subject Classification ID: 30F60
zbMATH DE Number: 6135749
zbMATH Keywords: universal Teichmüller space
zbMATH Keywords: BMOA
zbMATH Keywords: VMOA
zbMATH Keywords: Carleson measure
zbMATH Keywords: quasiconformal welding
MaRDI profile type: Publication
full work available at URL: j.aim.2012.10.017
OpenAlex ID: W2035258582
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DOI: 10.1016/J.AIM.2012.10.017
description: scientific article; zbMATH DE number 6135749