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 result recovers the best known constants of the classical polynomial inequality provided in \cite{bps}.
Cite
@article{arxiv.1405.1204,
title = {A subexponential vector-valued Bohnenblust-Hille type inequality},
author = {N. Albuquerque and D. Núñez-Alarcón and D. M. Serrano-Rodríguez},
journal= {arXiv preprint arXiv:1405.1204},
year = {2015}
}