Composition Operators From U-bloch Space To V-bloch Space On The First Hua Domain

In 1998,Professor Yin Weiping introduced the Cartan-Hartogs domain,followed by the creation of the Cartan-Egg domain.Hua domain,generalized Hua domain and Hua structure.The latter kind of domain is the first kind of domain's promotion.These five categories are referred to as Hua domain.Since the Hua domain was created,a lot of research groups have studied a lot of results.Under the guidance of a tutor,a new definition for the weighted Bloch spaces?u(HEI)is given on the first Hua domainHEI.Then we obtain a new generalized Hua's inequality corresponding to the first Hua domainsHEI.The boundedness and compactness of composition operator C?from u-Bloch space?u(HEI)to u-Bloch space ?v(HEI)are given by the generalized Hua's inequality and the constructed test function,and the sufficient conditions and necessary conditions are respectively obtained.Hereu?0,u?0.The paper consists of four chapters:In Chapter 1,we mainly introduce the preliminary knowledge of this article,the development of theory of analytic functions of several variables,researching back-ground in this paper;In Chapter 2,we mainly give some lemmas which will be used to proof the fol-lowing theorems in this paper including the generalized Hua's inequality;In Chapter 3,we mainly proof the boundedness of composition operator C? from the u-Bloch space ?u(HEI)to the v-Bloch space ?v(HEI)in the HEI;In Chapter 4,we mainly proof the compactness of composition operator C? from the u-Bloch space ?u(HEI)to the v-Bloch space ?v(HEI)in the HEI.