Optimal constants for the mixed $\left(\ell_{\frac{p}{p-1}}, \ell_2\right)$-Littlewood inequality

Tony Nogueira

Published 2016-04-21Version 1

For $p > 2.18006$ we prove that optimal constants for the mixed $\left( \ell _{\frac{p}{p-1}},\ell _{2}\right) $-Littlewood inequality for real-valued $m$% -linear forms on $\ell _{p}\times c_{0}\times \dots \times c_{0}$ are $% \left( 2^{\frac{1}{2}-\frac{1}{p}}\right) ^{m-1}.$ As far as we know, this is the first example of Hardy--Littlewood inequalities for $m$-linear forms with optimal constants with exponential growth.