Teichmüller space of circle diffeomorphisms with Hölder continuous derivatives

Based on the quasiconformal theory of the universal Teichmuller space, we introduce the Teichmuller space of diffeomorphisms of the unit circle with α-Holder continuous derivatives as a subspace of the universal Teichmuller space. We characterize such a diffeomorphism quantitatively in terms of the complex dilatation of its quasiconformal extension and the Schwarzian derivative given by the Bers embedding. Then, we provide a complex Banach manifold structure for it and prove that its topology coincides with the one induced by local C1+α-topology at the base point.