The Bohnenblust-Hille inequality was obtained in 1931 and (in the case of real scalars) asserts that for every positive integer $N$ and every $m$-linear mapping $T:\ell_{ \infty}^{ N}\times...\times\ell_{ \infty}^{ N}\rightarrow \mathbb{ R}$ one has (\sum\limits_{ i_{ 1},...,i_{ m}=1}^{ N}|T(e_{ i_{ ^{ 1}}},...,e_{ i_{ m}})|^{ \frac{ 2m}{ m+1}})^{ \frac{ m+1}{ 2m}}\leq C_{ m}\VertT\Vert, for some positive constant $C_{ m}$. Since then, several authors obtained upper estimates for the values of $C_{ m}$. However, the novelty presented in this short note is that we provide lower (and non-trivial) bounds for $C_{ m}$.
Categories: math.FA
