The upper estimates for the optimal constants of the multilinear Bohnenblust--Hille inequality obtained in [J. Funct. Anal. 264 (2013), 429--463] are here improved to: {0.1cm} {enumerate} For real scalars: Kn≤2(n−1)0.526322. For complex scalars: Kn≤π2(n−1)0.304975.{enumerate} {0.1cm} \noindent We also obtain sharper estimates for higher values of n. For instance, Kn<1.30379(n−1)0.526322 for real scalars and n>28 and Kn<0.99137(n−1)0.304975 for complex scalars and n>215.
@article{arxiv.1302.0517,
title = {On the optimal multilinear Bohnenblust--Hille constants},
author = {D. Nunez-Alarcon and D. Pellegrino and J. B. Seoane-Sepulveda and D. M. Serrano-Rodriguez},
journal= {arXiv preprint arXiv:1302.0517},
year = {2013}
}