HANKEL OPERATORS AND WEAK FACTORIZATION FOR HARDY-ORLICZ SPACESReport as inadecuate




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

Abstract : We study the holomorphic Hardy-Orlicz spaces H^ΦΩ, 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 ^1Ω ⊂ 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 BMOAΩ. As a consequence, we characterize those Hankel operators which are bounded from H ^ΦΩ into H^1 Ω.

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





Author: Aline Bonami - Sandrine Grellier -

Source: https://hal.archives-ouvertes.fr/



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