Hankel Operators and Weak Factorization for Hardy-Orlicz Spaces

2009/02/12 by Aline Bonami, Bonami, Aline, Sandrine Grellier +1
Mathematics · #32A35 #32A37 #47B3 #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #math.CA #math.CV #msc:32A35 #msc:32A37 #msc:47B3

paper · pdf · doi:10.48550/arxiv.0902.2138

arxiv created 2009/02/12 · arxiv updated 2009/12/01

Abstract

We study the holomorphic Hardy-Orlicz spaces H^Φ(Ω), where Ωis the unit ball or, more generally, a convex domain of finite type or a strictly pseudoconvex domain in Cn . The function Φis 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(Omega). As a consequence, we characterize those Hankel operators which are bounded from H ^Φ(Ω) into H¹ (Ω).

Related

• Hankel operators on holomorphic Hardy-Orlicz spaces
• Factorization of Hardy-Orlicz Space on the Disk and applications to Hankel Operators
• Atomic decomposition and Weak Factorization for Bergman-Orlicz spaces
• Atomic decomposition and weak factorization in generalized Hardy spaces of closed forms
• Duality for large Bergman-Orlicz spaces and Boundedness of Hankel Operators