On the mixed $\left( \ell _{1},\ell _{2}\right)$-Littlewood inequality for real scalars and applications

TL;DR

This paper derives sharp bounds for the mixed ,-Littlewood inequality for real scalars and applies these results to obtain optimal constants in related multilinear inequalities.

Contribution

It provides the first sharp estimates for the mixed ,-Littlewood inequality and extends these findings to determine optimal constants for certain 3-linear Bohnenblust--Hille inequalities.

Findings

Sharp estimates for the mixed ,-Littlewood inequality.

Optimal constants for a family of 3-linear Bohnenblust--Hille inequalities.

Applications to multilinear analysis and inequality bounds.

Abstract

In this paper we obtain the sharp estimates for the mixed $\left( \ell_{1},\ell _{2}\right) $-Littlewood inequality for real scalars with exponents $\left(2,1,2,2....,2\right) .$ These results are applied to find sharp estimates for the constants of a family of $3$-linear Bohnenblust--Hille inequalities with multiple exponents.