DECOMPOSITION THEOREMS FOR HARDY SPACES ON CONVEX DOMAINS OF FINITE TYPE

In this paper we study the holomorphic Hardy spaces H p(Ω), where Ω is a convex domain of finite type in C n. We show that for 0 < p ≤ 1, the space H p(Ω) admits an atomic decomposition. Moreover, we prove the following weak factorization theorem. Each f ∈ H p(Ω) can be written as f a sum of fj gj , where fj ∈ H 2p, gj ∈ H 2p. Finally, we extend these theorems to a class of domains of finite type that includes the strongly pseudoconvex domains and the convex domains of finite type.