Composition Operators From U-bloch Space To V-bloch Space On The Two Hua Domains

The operator theory on Holomorphic function space is the product of the combi-nation of complex analysis and functional analysis,people mainly study the bounded-ness,compactness,essential modulus estimation and spectrum of composition operator of different function spaces,etc.And they achieved a lot of good results.In this paper,we study the properties of some operators in the Hua domain introduced by Professor Yin Weiping.In 1998,Professor Yin Weiping introduced the Cartan-Hartogs domain,fol-lowed by the creation of the Cartan-Egg domain,and then he introduced a more ex-tensive Hua domain.However he found that the Hua domain can extends again,then he introduced the generalized Hua domain.In the base of the generalized Hua domain he extended that to the Hua Construction by now.The latter domain is the extension of the previous domain.These five categories are referred to as Hua domain.Under the guid-ance of a tutor,a new definition for the weighted Bloch spaces Bu(HE?),Bu(HC?)is given on the third Hua domain HE? and fourth Hua Construction HC? respec-tively.The boundedness and compactness of composition operator C?from u-Bloch space Bu(HE?)to v-Bloch space Bu(HE?)and u-Bloch space Bu(HC?)to v-Bloch space Bu(HC?)are given by the generalized Hua's inequality and the con-structed test function,and the sufficient conditions and necessary conditions are respec-tively obtained.Here u?0?v?0.The paper consists of six chapters:In Chapter 1,we introduce some background of analytic functions of several vari-ables;In Chapter 2,we mainly give some useful and important lemmas which can help us proving the theorem in this paper;In Chapter 3,we prove the boundedness of composition operator between the weighted Bloch spaces on the HE? by our methods;In Chapter 4,we prove the boundedness of composition operator between the weighted Bloch spaces on the HE? by our methods;In Chapter 5,we prove the boundedness of composition operator between the weighted Bloch spaces on the HC? by our methods;In Chapter 6,we prove the compactness of composition operator between the weighted Bloch spaces on the HC? by our methods.