Products Of Differentiation And Composition Operators On Some Analytic Function Spaces

In this thesis we study the compactness of products of di?erentiation andcomposition operators on several analytic function spaces.In Chapter 1, we introduce the history of operator theory, mainly givingthe definitions, background and some known results of the operators related tothis thesis.In Chapter 2, we study the products of di?erentiation and compositionoperators DC?on Bloch space and give a new and simple compactness char-acterization of DC?. We also show that our compactness condition in thesis issharp by giving an example.In Chapter 3, we concentrate on the products of di?erentiation and compo-sition operators C_?D~m on Bloch space. Some su?cient and necessary conditionsfor the compact operator C_?D~m on Bloch space are obtained.In Chapter 4, we are devoted to investigate C_?D~m on Dirichlet and BMOAspaces. Firstly, we discuss the compact conditions of C_?D~m : D?BMOA byNevanlinna counting function and Carleson measure. Secondly, by the compact-ness characterization of C_?D~m on BMOA we obtain, we study the properties ofthe compact operator C_?D~m on BMOA.