Absolutely summing Carleson embeddings on weighted Fock spaces with A∞-type weights

In this paper, we investigate the r-summing Carleson embeddings on weighted Fock spaces Fpα,w. By using duality arguments, translating techniques and block diagonal operator skills, we completely characterize the r-summability of the natural embeddings Id:Fpα,w→Lpα(μ) for any r⩾1 and p>1, where w is a weight on the complex plane \C that satisfies an Ap-type condition. As applications, we establish some results on the r-summability of differentiation and integration operators, Volterra-type operators and composition operators. Especially, we completely characterize the boundedness of Volterra-type operators and composition operators on vector-valued Fock spaces for all p∈(0,∞), which were left open before for the case p∈(1,2).