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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
  • http://hal.archives-ouvertes.fr/hal-00360774
  • oai:hal.archives-ouvertes.fr:hal-00360774
  • From: Sandrine Grellier <>
  • Submitted on: Wednesday, 11 February 2009 21:04:28
  • Updated on: Thursday, 12 February 2009 16:53:18