Rigidity of Volterra-type integral operators on Hardy spaces of the unit ball

2020/04/27 by Santeri Miihkinen, Miihkinen, Santeri, Jordi Pau +5
Mathematics · #Advanced Harmonic Analysis Research #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2004.12671

openalex publication_date 2020/04/27 · openalex created_date 2020/05/01 · openalex updated_date 2026/07/28

Abstract

We establish that the Volterra-type integral operator J_b on the Hardy spaces H^p of the unit ball \mathbbB_n exhibits a rather strong rigid behavior. More precisely, we show that the compactness, strict singularity and ℓ^p-singularity of J_b are equivalent on H^p for any 1 ≤ p < ∞. Moreover, we show that the operator J_b acting on H^p cannot fix an isomorphic copy of ℓ² when p ≠ 2.

Related

• Strict singularity of a Volterra-type integral operator on H^p
• Structural rigidity of generalised Volterra operators on H^p
• Integration operators between Hardy spaces on the unit ball of \Cn
• Strict singularity of Volterra type operators on Hardy spaces
• Volterra type integration operators from Bergman spaces to Hardy spaces