A subexponential vector-valued Bohnenblust–Hille type inequality

Bayart, Pellegrino and Seoane recently proved that the polynomial Bohnenblust–Hille inequality for complex scalars is subexponential. We show that a vector-valued polynomial Bohnenblust–Hille inequality on complex Banach lattices is also subexponential for some special cases. Our main result recovers the best known constants of the classical polynomial inequality provided in [4].