Composition Operators On The Weighted Bloch Spaces On The First Type Of The Classical Bounded Symmetric Domains

In this paper, we give a new definition for the weighted Bloch spaces on the first type of classical bounded symmetric domains, which is denoted by βp(RI(m, n)), p≥0. Then we prove the equivalence of the norms f 1,pand f 2,p. Mainly, we study the compactness of composition operator Cφfrom βp(RI(m, n)) to βq(RI(m, n)). We obtain a sufficient and necessary condition for Cφ: βp(RI(m, n))â†'βq(RI(m, n)) tobe compact.The paper consists of five chapters:In Chapter 1, we introduce the development of theory of analytic functions of several variables, researching background, and the corresponding preliminary knowledge;In Chapter 2, we mainly discuss the equivalence of the norms f 1,pand f 2,pdefined in this paper and [32];In Chapter 3, we state several auxiliary results most of which will be used in the proofs of the main results;In Chapter 4, we mainly discuss the compactness of the composition operator from the p-Bloch space to the q-Bloch space.