Composition Operators On The Weighted Bergman Space With Exponential Type Weights

In this thesis, we mainly study the properties of Volterra type operator and composition operator on the weighted Bergman space AL2ψ,(D) with exponential type weights. For certain class of subharmonic ψ:B�' R, we show the the nec-essary and sufficient condition of boundedness and compactness for Volterra type operator Vgψ from the weighted Bergman space.AL2ψ(D) to Bloch type space (and little Bloch type space Bψ,0(D)). We also obtain the boundedness、compactness and Schatten class of composition operator on the,Bergman space ALψ2(D) and Bergman space AL2ψ(C).In chapter 1, we discuss some related research background, and give some basic concepts and notations. At last, we show the significance of the research work.In chapter 2, we characterize the condition of boundedness and compactness for Volterra type operator from the weighted Bergman spaceAL2ψ (D) with expo-nential type weights to Bloch type space(and little Bloch type space Bψ,0(D)).In chapter 3, we discuss the boundedness、compactness and Schatten class of composition operator on the weighted Bergman space AL2ψ(D) with exponen-tial type weights.In chapter 4, we show the boundedness and compactness of composition operator on the weighted Bergman space AL2ψ(C) with exponential type weights.