Composition Operators With Quasiconformal Symbols On Weighted Bergman Spaces

In this paper, we study the composition operator with the symbol function being a quasicon-formal mapping on the unit disk, acting on the weighted Bergman space L_a~2(dAa). We use the quasiconformal mapping function properties to describe the corresponding operator properties of the composition operator, i.e. the boundedness, compactness, Sp and estimate the essential norm.In the chapter one, some backgrounds and main results are given.In the chapter two and three, the sufficient and necessary conditions for the boundedness, compactness and estimate the norm of a composition operator with the symbol function being a quasiconformal mapping on the unit disk, acting on the weighted Bergman space L_a~2(dAa).In the chapter four and five, the sufficient conditions for the Sp class operator and the suffi-cient and necessary conditions for the bounded below of a composition operator with the symbol function being a quasiconformal mapping on the unit disk, acting on the weighted Bergman space L_a~2(dAa).