Quasiconformality of harmonic extensions
type: Item
instance of: scholarly article
title: Quasiconformality of harmonic extensions
zbMATH Open document ID: 0951.30017
DOI: 10.1016/S0377-0427(99)00009-6
author: Dariusz Partyka
author: Ken-Ichi Sakan
published in: Journal of Computational and Applied Mathematics
publication date: 2000-12-18T00:00:00Z
review text: Let \(\Hom^+({\mathbb T})\) denote the class of all sense preserving homeomorphic self-mappings of the unit circle \({\mathbb T}\). The authors show that a homeomorphism \(\gamma\in\Hom^+({\mathbb T})\) with bounded derivative has a quasi-conformal extension, if and only if, its derivative is bounded away from zero and the Cauchy-Stieltjes transform of its differential is bounded. It is also shown that the foregoing result extends an earlier result due to \textit{O. Martio} [Ann. Acad. Sci. Fenn., Ser. A. I. Math. 425, 1-10 (1968; Zbl 0162.37902)].
Mathematics Subject Classification ID: 30C62
Mathematics Subject Classification ID: 30C55
zbMATH DE Number: 1334884
zbMATH Keywords: harmonic
zbMATH Keywords: quasiconformal mappings
zbMATH Keywords: Poisson integral
reviewed by: H. P. Dikshit
MaRDI profile type: Publication
cites work: Q4896310
cites work: Q5618011
cites work: Q3922907
cites work: Planar Harmonic Maps with Inner and Blaschke Dilatations
cites work: Q5546089
cites work: Q4357161
cites work: Q4266740
cites work: Q3234668
cites work: Q5516901
cites work: On multipliers preserving convergence of trigonometric series almost everywhere
description: scientific article; zbMATH DE number 1334884