HANKEL OPERATORS AND WEAK FACTORIZATION FOR HARDY-ORLICZ SPACES

Aline Bonami (1) , Sandrine Grellier (1)

1 MAPMO - Mathématiques - Analyse, Probabilités, Modélisation - Orléans

We study the holomorphic Hardy-Orlicz spaces H^Φ(Ω), where Ω is the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn . The function Φ is in particular such that H ^1(Ω) ⊂ H^Φ (Ω) ⊂ H ^p (Ω) for some p > 0. We develop for them maximal characterizations, atomic and molecular decompositions. We then prove weak factorization theorems involving the space BMOA(Ω). As a consequence, we characterize those Hankel operators which are bounded from H ^Φ(Ω) into H^1 (Ω).

Mots clés: Hankel operator; Hardy Orlicz spaces; atomic decomposition; finite type domains; weak factorization; logarithmic mean oscillation; BMO with weights; Hankel operator.

Domaines: Variables complexes [math.CV]; Analyse classique [math.CA]; Equations aux dérivées partielles [math.AP]

Aline Bonami, Sandrine Grellier. HANKEL OPERATORS AND WEAK FACTORIZATION FOR HARDY-ORLICZ SPACES. Colloquium Mathematicum, 2010, 118, pp.107-132. ⟨hal-00360774⟩