Schwarz-Pick Estimates For Bounded And Positive Real Part Holomorphic Functions On Several Types Of Reinhardt Domains

It is natural to consider an extension of the classical Schwarz-Pick estimates to higher dimensions. In recent years, many good results have been received. In this thesis, we study Schwarz-Pick estimates for bounded and positive real part holomorphic functions on several types of Reinhardt domains. It consists of three chapters.In the first chapter, we briefly introduce the. background and the development of Schwarz-Pick estimates in several complex variables, some notations, definitions and the main results of this thesis.In Chapter 2, we first obtain Schwarz-Pick estimates for bounded holomorphic func-tions on Bn ×Bm. On the basis of the results in the proof, we gain Schwarz-Pick estimates for bounded holomorphic functions on Bn1×Bn2 ×...× Bnm. We generalize the early work on Schwarz-Pick estimates for bounded holomorphic functions on the polydisk and get a better estimate. And we also study Schwarz-Pick estimates for positive real part holomorphic functions on these Reinhardt domains.In Chapter 3, by applying a method which is similar to that in chapter 2, we gain the estimates for bounded and positive real part holomorphic functions on some special points of two types of Reinhardt domains.