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HANKEL OPERATORS AND WEAK FACTORIZATION FOR HARDY-ORLICZ SPACES

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).
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https://hal.archives-ouvertes.fr/hal-00360774
Contributor : Sandrine Grellier <>
Submitted on : Wednesday, February 11, 2009 - 9:04:28 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
Document(s) archivé(s) le : Tuesday, June 8, 2010 - 10:17:25 PM

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  • HAL Id : hal-00360774, version 1
  • ARXIV : 0902.2138

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

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