Generalization Of Hua’s Inequalities And An Application

We use the existing techniques and Schur’s unitary triangularization theorem to generalize Hua’s inequality. Then we mainly use the new inequality, decompose polar coordinate and an automorphism in YI(N, m, n; K) to discuss the boundedness of composition operator Cφfrom the p-Bloch space to the q-Bloch space, where YI(N, m, n; K) denotes the first Cartan-Hartogs domain, and p ≥ 0, q ≥ 0.The paper consists of four chapters:In Chapter 1, we mainly introduce the development of theory of analytic functions of several variables, researching background in this paper;In Chapter 2, we mainly give some lemmas which will be used to proof the following theorems in this paper;In Chapter 3, we mainly generalize a new Hua’s inequality by using the lemmas given in Chapter 2 and some new methods;In Chapter 4, we mainly proof the boundedness of composition operator Cφfrom the p-Bloch space to the q-Bloch space by using the generalization of Hua’s inequality given in Chapter 3.