Composition Type Operators On Weighted Bloch Spaces

In this thesis, we mainly study the boundedness and compactness of composition operators on some analytic function spaces on the unit disc.To study the boundedness and compactness of composition operators, we mainly use their definitions and some properties of the norm to find the condition that u andφsatisfied, we also choose some appropriate auxiliary function. The Schwarz-Pick lemma and weak convergence lemmas in corresponding functional spaces are often needed.First, we study the boundedness and compactness of weighted composition operators on weighted Bloch spaces on the unit disc and obtain necessary and sufficient conditions of the boundedness and compactness, which improve the result of S. Ohno and R. Zhao.Second, we discuss the boundedness and compactness of weighted composition operators on the little weighted Bloch space in unit disc, and obtain necessary and sufficient conditions of the boundedness and compactness.At last, inspired by a question raised by C.C.Cowen and B.D.MacCluer, we discovered an meaningful conclusions, which characterized the boundedness and compactness on a new composition type operators on the Bloch spaces on the unit disc and obtain necessary and sufficient conditions of the boundedness and compactness, and also gave some corollaries.