Duality for large Bergman-Orlicz spaces and Boundedness of Hankel Operators

2015/01/14 by Benoît F. Sehba, Benoit F. Sehba, Sehba, Benoit F. +2
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #math.CA #math.CV

paper · pdf · doi:10.48550/arxiv.1501.03416

arxiv created 2015/01/14 · openalex publication_date 2015/01/14 · arxiv updated 2015/01/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For \mathbb Bⁿ the unit ball of \mathbb Cⁿ, we consider Bergman-Orlicz spaces of holomorphic functions in L^Φ_α, which are generalizations of classical Bergman spaces. We characterize the dual space of large Bergman-Orlicz space, and bounded Hankel operators between some Bergman-Orlicz spaces A_α^Φ₁(\mathbb Bⁿ) and A_α^Φ₂(\mathbb Bⁿ) where Φ₁ and Φ₂ are either convex or concave growth functions.

Citations

• Generalizations of Lipschitz spaces and an application to Hardy spaces and bounded mean oscillation

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