Universal Teichmüller Space And Q_K（p,q） Space And Related Results

Universal Teichmüller space T contains all Riemann surfaces as complex submanifold,and is important in the theory of quasiconformal Teichmüller space.Recently,it is popular to characterize some subspaces of universal Teichmüller spaces by means of quasiconformal Teichmüller space theory.This paper characterize the Schwarzian derivative model and the Bers projection of QK(p,p-2)-Teichmüller space.Integrable asymptotic affine homeomorphisms corresponds to the subspace of universal Teichmüller space.We characterize the properties of p-integrable asymptotic affine homeomorphisms and give a necessary condition for a quasisymmetric homeomorphisms of S1 to be a p-integrable asymptotic affine homeomorphisms.Qp,0 space is a special case of the analytic function space QK(p,q),and the properties of the analytic function space QK(p,q)is the basis of the QK(p,p-2)-Teichmüller space.We study the properties of the analytic function space Qp,0,then provide a discriminative criterion.The following are the main contents of this paper:Chapter1,research background and related preparation.We briefly introduces the necessary knowledge of preparation.It mainly includes Carleson measure、Bers projection、quasiconformal map、quasisymmetric map and its extension、definition and basic properties of universal Teichmüller space,and definition and basic properties of some analytic functions spaces.Chapter2,by means of quasiconformal Teichmüller space theory,we characterize the Schwarzian derivative model and Bers projection ofQK(p,p2)-Teichmüller space.Chapter3,we decribe the properties of p-integrable asymptotic affine homeomorphisms and give a necessary condition for a quasisymmetric homeomorphisms of S1 to be a p-integrable asymptotic affine homeomorphisms.Chapter4,we study the properties of the analytic function space Qp,0,then provide a discriminative criterion.