Volterra operators between Hardy spaces of vector-valued Dirichlet series

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.