| 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. |
