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arXiv · 2004.12671

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

Santeri Miihkinen·Jordi Pau·Antti Perälä·Maofa Wang
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Abstract

We establish that the Volterra-type integral operator $J_b$ on the Hardy spaces $H^p$ of the unit ball $\mathbb{B}_n$ exhibits a rather strong rigid behavior. More precisely, we show that the compactness, strict singularity and $\ell^p$-singularity of $J_b$ are equivalent on $H^p$ for any $1 \le p < \infty$. Moreover, we show that the operator $J_b$ acting on $H^p$ cannot fix an isomorphic copy of $\ell^2$ when $p \ne 2.$

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Santeri Miihkinen, Jordi Pau, Antti Perälä, Maofa Wang. 2020-04-27. Rigidity of Volterra-type integral operators on Hardy spaces of the unit ball. https://arxiv.org/abs/2004.12671

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