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 logf′ 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 logf′ belongs to either some Qp,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.
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