On Teichmuller space of circle diffeomorphisms with Holder continuous derivative

Matsuzaki [M1] introduced the Teichmuller space T-0(alpha) of diffeomorphisms of the unit circle with Holder continuous derivatives and investigated its Schwarzian derivative model. This paper deals with the pre-Schwarzian derivative model T-0(alpha)(1) of the Teichmuller space T-0(alpha). It is shown that T-0(alpha)(1) is a connected open subset of B-0(alpha)(Delta) and the pre-Bers projection is a holomorphic split submersion in T-0(alpha).