The Closure Of Dirichlet Type Spaces In The Bloch Type Space And Related Operator Theory

Closure problem and operator theory are important parts of complex analysis.Since Anderson,et al proposed the closure problem in Bloch spaces,although it has not been solved,the related closure problem has become an important research field for many scholars at home and abroad.And the linear operator is one of the topic issues in the academic field.In this thesis,the composition operator and the closure of Dirichlet type spaces in the Bloch type space,the topological structure of linear operators from Bloch type spaces to the disk algebra,new characterizations of linear operators from F(p,q,s)spaces into Bloch type spaces and new characterizations of linear operators from Hardy spaces to Zygmund type spaces are investigated.The thesis consists of five chapters.Chapter 1 is concerned in the research background;the definitions of some holomorphic function spaces and some notations are given.Chapter 2 is concerned in characterizations of the closure of Dirichlet type spaces in the Bloch type space.This result is applied to the Blaschke product.Further,basic properties of composition operators from Bloch type spaces to the closure are given.Chapter 3 is aimed at studying some estimates of weighted composition operators from Bloch type spaces to the disk algebra.At the same time,we investigate the path connectedness of the space of such operators and obtain the related results about path connectedness.Chapter 4 is concentrated at investigating linear operators from to Bloch type spaces.We obtain some estimates for the essential norm of the operator.In addition,new characterizations for basic properties of such operators are given.Chapter 5 is devoted to investigate linear operators from Hardy spaces to Zygmund type spaces.Also,we obtain new characterizations for basic properties of such operators and some estimates for the essential norm of such operators.