The Khintchine Inequality is equivalent to the Mixed $\left( \ell_{\frac{p}{p-1}},\ell_{2}\right) $-Littlewood Inequality

Daniel Núñez-Alarcón, Diana M. Serrano-Rodríguez

Published 2017-04-04Version 1

In this paper we prove that the Khintchine Inequality is equivalent to the mixed $\left( \ell_{\frac{p}{p-1}},\ell_{2}\right) $-Littlewood inequality. Moreover, we obtain the optimal constants of the Multiple Khintchine inequality. As application, we obtain the optimal constants of the multilinear mixed $\left( \ell_{\frac{p}{p-1}},\ell_{2}\right) $-Littlewood inequality, completing the estimates in \cite{racsam}.