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arXiv · 1205.0759

On $H^\infty$ on the complement of C^{1+α} curves

María José González Fuentes·José Manuel Enríquez de Salamanca García
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Abstract

Let $ρ$ be a quasiconformal mapping on the plane with complex dilatation $μ$. We show that if $μ$ satisfies a certain Carleson measure condition, then one can transfer $H^{\infty}$ on the upper half plane onto the corresponding space in the complement of the quasicircle $Γ=ρ(\mathbb{R})$, and that this condition on $μ$ characterizes $C^{1+α}$ curves.

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María José González Fuentes, José Manuel Enríquez de Salamanca García. 2014-01-22. On $H^\infty$ on the complement of C^{1+α} curves. https://arxiv.org/abs/1205.0759

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