Hankel Bilinear forms on generalized Fock-Sobolev spaces on \mathbb Cⁿ

2019/12/19 by Carme Cascante, Cascante, Carme, Joan Fàbrega +3
Mathematics · #Advanced Algebra and Geometry #Classical Analysis and ODEs (math.CA) #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Geometry and complex manifolds #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.1912.09241

openalex publication_date 2019/12/19 · openalex created_date 2019/12/26 · openalex updated_date 2026/07/28

Abstract

We characterize the boundedness of Hankel bilinear forms on a product of generalized Fock-Sobolev spaces on \mathbb Cⁿ with respect to the weight (1+|z|)^ρe^-\fracα2|z|^2ℓ, for ℓ≥ 1, α>0 and ρ∈\mathbb R. We obtain a weak decomposition of the Bergman kernel with estimates and a Littlewood-Paley formula, which are key ingredients in the proof of our main results. As an application, we characterize the boundedness, compactness and the membership in the Schatten class of small Hankel operators on these spaces.

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• Small Hankel operators on generalized Fock spaces
• Hankel operators on the Fock-Sobolev spaces
• Bounded Hankel products on Fock-Sobolev spaces
• Small Hankel operators on vector valued generalzed Fock spaces
• Big Hankel operators on vector-valued Fock spaces in \C^d