The Weighted Composition Operator On BMOA Space And Bloch-type Space In The Unit Ball

The dissertation collects the main results obtained by the author Master's Degree. This study mainly concerns the weighted composite operator on BMOA space and Bloch-type space in n-dimension unit ball and discusses the bounded-ness, compactness and the essential norm of the weighted composition operator.The first chapter gives the research background of BMOA space, Bloch-type space in the unit ball and the weighted composite operator. Then it gives some notations, conceptions and theorems that are necessary in the thesis. At the same time, it introduces the significance of this research.The second chapter studies the weighted composite operator from BMOA space to Bloch-type space in the unit ball. For the research of the weighted composition operator from BMOA space to Bloch space, Li Songxiao has given the sufficient and necessary condition for the weighted composition operator to be bounded in the unit disc in the reference [1]. S.Ohno has given the sufficient and necessary condition for the weighted composition operator in Bloch space and in the little Bloch space to be bounded and compact in the unit disc in the reference [2]. In this chapter, the results collected from above are used in the unit ball and Bloh-type space.In the third chapter, the author studies the weighted composite operator from BMOA space to little Bloch-type space in the unit ball. This chapter is the gener-alization of the results in the reference [3], discussing the sufficient and necessary condition for the weighted composite operator to be bounded or compact in the unit ball.The fourth chapter studies the essential norm of the weighted composition operator in different Bloch-type space in the unit ball, and gives the upper bound and lower bound of the essential norm of the weighted composition operator.