DECOMPOSITION THEOREMS FOR HARDY SPACES ON CONVEX DOMAINS OF FINITE TYPE

Sandrine Grellier (1) , Marco Peloso (2)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans
2 Polito - Politecnico di Torino = Polytechnic of Turin

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.

Mots clés: Hardy spaces; atomic decomposition; finite type domains; convex domains.

Mots clés: convex domains

Domaines: Variables complexes [math.CV]

Sandrine Grellier, Marco Peloso. DECOMPOSITION THEOREMS FOR HARDY SPACES ON CONVEX DOMAINS OF FINITE TYPE. Illinois Journal of Mathematics, 2002, 46, pp.207-232. ⟨hal-00076918⟩