# The best constants in the Multiple Khintchine Inequality

## TL;DR

This paper determines the optimal constants in the multiple Khintchine inequality, enabling precise bounds in related inequalities and completing a line of research initiated by Pellegrino.

## Contribution

It provides the exact best constants for the multiple Khintchine inequality, advancing the understanding of related inequalities in analysis.

## Key findings

- Established the optimal constants for the multiple Khintchine inequality.
- Derived the best constants for the mixed (ℓ_{p/(p-1)}, ℓ_2)-Littlewood inequality.
- Resolved a problem previously studied by Pellegrino.

## Abstract

In this work we provide the best constants of the multiple Khintchine inequality. This allows us, among other results, to obtain the best constants of the mixed $\left( \ell_{\frac{p}{p-1}},\ell_{2}\right) $-Littlewood inequality, thus ending completely a work started by Pellegrino in \cite{pell}.