The Equivalent Characterization On Zygmund Spaces And The Atomic Decomposition On Bloch Type Spaces In C~n

In this dissertation, we will study several equivalent characterizations of the μ-Zygmund space and atomic decomposition of the μ-Bloch space on the unit ball in Cn. At the same time, integral representation for the function on the μ-Bloch space and dual relationship between the μ-Bloch space and the Bergman space will be given.This dissertation consists of three chapters.In the first chapter, we will take a comprehensive summary about the research background and the conclusions that were given.In the second chapter, we will study four kinds of equivalent characteri-zations of the μ-Zygmund space on the unit ball, that is theorem 2.3.1.In the third chapter, we will study atomic decomposition of the μ- Bloch space on the unit ball, that is theorem 3.3.1.In order to solve this problem, firstly, integral representation for the μ-Bloch space function will be given, that is theorem 3.3.1, next, dual relationship between the μ-Bloch space and the normal weighted Bergman space will be given, that is theorem 3.3.2.