Abstract: 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 Cⁿ, 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 d uality 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

Key words: Integral mean, Dini function, b_k-weight function, Boundary value, Duality