多复变函数论是当代基础数学的主流方向之一，而全纯函数空间理论和几何函数论是其重要的组成部分。本项目以多复变数全纯Campanato空间和Schwarz引理作为研究对象，拟用多复变、调和分析、微分几何和李代数等现代数学工具，研究高维复单位球上全纯Campanato空间的前对偶空间及其上的相关算子的有界性和紧性等问题；讨论一般强拟凸域上全纯Campanato空间的Gleason 及Corona问题的可解性; 建立有界对称域上的边界型Schwarz引理和高阶Schwarz-Pick估计。本项目研究的内容新颖, 交叉性和基础性强，项目组将在已获得的前期工作基础上，沿着当前多复变领域的若干热点和难点问题进行集体攻关，本项目的成果将进一步丰富和完善当前多复变函数论的研究。

Function theory of several complex variables is one of main directions in mordern mathematics, analytic spaces and geometric function theory are two important parts of this field. This project deals with some important problems including holomorphic Campanato space and Schwarz lemma in high dimensions. Based on several complex variables, Harmonic Analysis, Differential Geometry and Lie Algebra, we will establish the pre-duals of holomorphic Campanato space and some operators study for boundedness and compactness defined on the unit ball in high dimesions. We will investigate the problems of the Gleason and Corona on holomorphic Campanato space defined in strongly pseudoconvex domains in several complex variables; we will establish the boundary Schwarz lemma and high order Schwarz-Pick estimate in the bounded symmetric domains. The project is aimed at the hot and difficult problems in a new growth point and crossover study. These results of the project, basing on our obtained reserach, may help to complete the study in function theory of several complex variables.