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