The Universal Teichmüller Space and Function Space

In this paper, a subspace TF02,1−s,s of the universal Teichmüller space, which is related to the analytic function space F02,1−s,s, is introduced and the holomorphy of the Bers map is shown. It is also proved that the pre-Bers map is holomorphic and the prelogarithmic derivative model T˜F02,1−s,s of TF02,1−s,s is a disconnected subset of the function space F02,1−s,s. Moreover, several equivalent descriptions of elements of TF02,1−s,s are obtained and the holomorphy of higher Bers maps is proved.

A Modified Analytic Function Space Feynman Integral and Its Applications

We analyze the generalized analytic function space Feynman integral and then defined a modified generalized analytic function space Feynman integral to explain the physical circumstances. Integration formulas involving the modified generalized analytic function space Feynman integral are established which can be applied to several classes of functionals.

Composition operators on Qp spaces

A holomorphic map ψ of the unit disk ito itself induces an operator Cψ on holomorphic functions by composition. We characterize bounded and compact composition operators Cψ on Qp spaces, which coincide with the BMOA for p = 1 and Bloch spaces for p > 1. We also give boundedness and compactness characterizations of Cψ from analytic function space X to Qp spaces, X = Dirichlet space D, Bloch space B or B0 = {f: f′ ∈ H∞}.