Research On Composition Operators On Bloch Type Spaces

Let Ω be a domain in Euclidean complex space Cn,(?) be a holomorphic self-map of Ω, and u be a holomorphic function on Ω. If f is an element of a holomorphic function space, a linear operator named composition operator which is induced by (?) is defined by C(?)f=fo(?), and a weighted composition operator is defined by uC(?)(f)=u·fo(?).In this thesis, isometry of composition operators on Bloch type space on the unit polydisc are firstly investigated. Then necessary and sufficient conditions for composi-tion operator to be isometric are obtained.Secondly, we give new estimates of essential norms of composition operators on the Bloch type spaces on the unit polydisc, as an application, we get a new characterization of the compact composition operator. Then we investigate the boundedness (here we call pullback properties) and compactness of composition operators from Bloch space to BMOA space.Finally, we focused on the topological structure and compact difference of compo-sition operators from Bloch type spaces to bounded holomorphic function spaces.