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

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Let $ho$ be a quasiconformal mapping on the plane with complex dilatation $\mu$. We show that if $\mu$ 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 $\Gamma= ho\mathbb{R}$, and that this condition on $\mu$ characterizes $C^{1+\alpha}$ curves.

Author: María José González Fuentes; José Manuel Enríquez de Salamanca García

Source: https://archive.org/