Generalized Composition Operators On Weighted Bloch Spaces And Weighted Litter Bloch Spaces

The background and present conditions are and summarized for the study of bound-edness and compactness of composition operator.At the same time,the most important theorems about the weighted Bloch Spaces and weighted Little Bloch Spaces have been listed,which provide train of thought for this paper.Let D be a unit circle in Euclidean complex spaces Cn, φ be a holomorphic self-map of D,and g be a holomorphic function on D.If f is an element of a holomorphic function spaces,a linear operator named composition operator which is induced by φ is denned by Cφf(z)= f o φ;and a generalized composition operator which is induced by φ and g is defined by Cφf(z)=f0zf/(φ(ξ))g(ξ)dξThis paper discusses the boundedness and compactness of the generalized composi-tion operator Cφg on weighted Bloch Spaces and weighted Little Bloch Spaces.The suffi-cient and necessary conditions of the boundedness and compactness are obtained.These complete related information about weighted Bloch Spaces and weighted Little Bloch S-paces,which makes us clear about the details and methods of proof of weighted Bloch Spaces and weighted Little Bloch Spaces.