DECOMPOSITION THEOREMS FOR HARDY SPACES ON CONVEX DOMAINS OF FINITE TYPE

Grellier, Sandrine; Peloso, Marco

HAL, hal-00076918 / Harvested from HAL

Résumé

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.

Publié le : 2002-07-05
Classification: Hardy spaces, atomic decomposition, finite type domains, convex domains., convex domains, 32A37 47B35 47B10 46E22, [MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]

@article{hal-00076918,
     author = {Grellier, Sandrine and Peloso, Marco},
     title = {DECOMPOSITION THEOREMS FOR HARDY SPACES ON CONVEX DOMAINS OF FINITE TYPE},
     journal = {HAL},
     volume = {2002},
     number = {0},
     year = {2002},
     language = {en},
     url = {http://dml.mathdoc.fr/item/hal-00076918}
}

Grellier, Sandrine; Peloso, Marco. DECOMPOSITION THEOREMS FOR HARDY SPACES ON CONVEX DOMAINS OF FINITE TYPE. HAL, Tome 2002 (2002) no. 0, . http://gdmltest.u-ga.fr/item/hal-00076918/