This is an announcement for the paper “The Khintchine Inequality is equivalent to the Mixed $(\ell_{\frac{p}{p-1}}, \ell_2)$-Littlewood Inequality” by Daniel Núñez-Alarcónhttps://arxiv.org/find/math/1/au:+Nunez_Alarcon_D/0/1/0/all/0/1, Diana M. Serrano-Rodríguezhttps://arxiv.org/find/math/1/au:+Serrano_Rodriguez_D/0/1/0/all/0/1.

Abstract: n this paper we prove that the Khintchine Inequality is equivalent to the mixed $(\ell_{\frac{p}{p-1}}, \ell_2)$-Littlewood inequality. Moreover, we obtain the optimal constants of the Multiple Khintchine inequality. As application, we obtain the optimal constants of the multilinear mixed $(\ell_{\frac{p}{p-1}}, \ell_2)$-Littlewood inequality, completing the estimates in \cite{racsam}..

The paper may be downloaded from the archive by web browser from URL https://arxiv.org/abs/1704.01029