Volterra operators between Hardy spaces of vector-valued Dirichlet series

Let 2≤ p<∞ 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 Hʷᵉᵃᵏₚ(X) to the Hardy space H⁺ₚ(X) of vector-valued Dirichlet series. To obtain this, a Littlewood--Paley inequality for Dirichlet series is established.