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hal-00360774, version 1

## HANKEL OPERATORS AND WEAK FACTORIZATION FOR HARDY-ORLICZ SPACES

Aline Bonami () 1, Sandrine Grellier () 1

(2009-02-11)

Abstract: 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).

• 1:  Mathématiques - Analyse, Probabilités, Modélisation - Orléans (MAPMO)
• Université d'Orléans – CNRS : UMR7349
• Domain : Mathematics/Complex Variables
Mathematics/Classical Analysis and ODEs
• Keywords : Hardy Orlicz spaces – atomic decomposition – ﬁnite type domains – weak factorization – logarithmic mean oscillation – BMO with weights – Hankel operator.

• hal-00360774, version 1
• oai:hal.archives-ouvertes.fr:hal-00360774
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• Submitted on: Wednesday, 11 February 2009 21:04:28
• Updated on: Thursday, 12 February 2009 16:53:18