中文摘要：

该文将几个全纯函数空间的定义从单复变数推广到多复变数，这些空间中全纯函数的增长性依赖于某个权函数．作者研究了它们的增长性与边界值的关系以及这些空间相互之间的对偶关系，所用方法和技巧与单复变数有不少区别．所得到的结论是单复变数许多已知结果的推广．

英文摘要：

In this paper, the authors generalize the definitions of several spaces of holomorphic functions from the unit disc in C to the unit ball in C^n, where the growth of holomorphic functions depends on a weight function. The authors investigate the relation between the growth and the boundary value of functions, and discuss the duality of these spaces. The results generalize many known ones in the unit disc, but the method and skill here are different from the case of the unit disc.