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: $K_{ n}\leq\sqrt{ 2}(n-1)^{ 0.526322}$. For complex scalars: $K_{ n}\leq\frac{ 2}{ \sqrt{ \pi}}(n-1)^{ 0.304975}$.{ enumerate} { 0.1cm} \noindent We also obtain sharper estimates for higher values of $n$. For instance, \[ K_{ n}<1.30379(n-1) ^{ 0.526322}\] for real scalars and $n>2^{ 8}$ and \[ K_{ n}<0.99137(n-1) ^{ 0.304975}\] for complex scalars and $n > 2^{ 15}.$
Categories: math.FA