Morrey type teichmü ller space and higher bers maps

In this paper, we focus on the set of univalent analytic functions f with log f′ ∈. Motivated by the study of BMO-Teichmuller spaces and Morrey type spaces, we establish serval equivalent characterizations of Morrey type domains. Furthermore, we show that the higher Bers maps, induced by the higher Schwarzian differential operators, are holomorphic in Morrey type Teichm uller spaces. Finally, one of connected components in the small pre-logarithmic derivative model of the Morrey type Teichm uller space is also obtained.