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arXiv · 2404.04896

Volterra operators between Hardy spaces of vector-valued Dirichlet series

Jiale Chen
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Abstract

Let $2\leq p<\infty$ and $X$ be a complex infinite-dimensional Banach space. It is proved that if $X$ is $p$-uniformly PL-convex, then there is no nontrivial bounded Volterra operator from the weak Hardy space $\mathscr{H}^{\text{weak}}_p(X)$ to the Hardy space $\mathscr{H}^+_p(X)$ of vector-valued Dirichlet series. To obtain this, a Littlewood--Paley inequality for Dirichlet series is established.

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Jiale Chen. 2024-04-07. Volterra operators between Hardy spaces of vector-valued Dirichlet series. https://doi.org/10.4153/s0008439524000705

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