Teichmüller space of circle diffeomorphisms with Zygmund smooth

Abstract We introduce and investigate the Teichmuller space T 0 Z of diffeomorphisms of the unit circle with Zygmund continuous derivatives. We first give some characterizations of such diffeomorphism by means of the complex dilatation of its quasiconformal extension and the logarithmic and Schwarzian derivatives of its normalization decomposition. Also, we characterize the quasicircle which corresponds to circle diffeomorphism with Zygmund continuous derivatives by conformal welding. Then, we investigate the logarithmic derivative model and Schwarzian derivative model of Teichmuller space T 0 Z . It is proved that the pre-Bers and Bers projections are holomorphic in T 0 Z and the logarithmic derivative model of T 0 Z is connected in B 0 Z ( Δ ) .