Quasiconformal properties of Qp, 0 curves and Dirichlet-type curves. (October 2022)

• Record Type: Journal Article
• Authors: González, María J.
• Is Part Of: Nonlinear analysis. Volume 223(2022)
• Publication Date: 2022-10
• Subjects: 30C35 -- 30C45 -- 30C62; Qp, 0 spaces -- Weil-Petersson curves -- Dirichlet space -- Quasiconformal mappings; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2022.113048
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: Let Γ be a closed Jordan curve, and f the conformal mapping that sends the unit disc D onto the interior domain of Γ . If log f ′ belongs to the Dirichlet space D, we call Γ a Weil-Petersson curve. The purpose of this note is to extend recent results, obtained by G. Cui and Ch. Bishop in the case of Weil-Petersson curves, to the case when log f ′ belongs to either some Q p, 0, space, for 0 < p ≤ 1, or to some weighted-Dirichlet space contained in D . More precisely, we will characterize the quasiconformal extensions of f, and describe some of the geometric properties of Γ, that arise in this context.