A short communication on the constants of the multilinear Hardy--Littlewood inequality

Abstract

It was recently proved that for $p>2m^3-4m^2+2m$ the constants of the Hardy--Littlewood inequality for $m$-linear forms on ${\ell }_p$-spaces are less than or equal to the best known estimates of respective constants of the Bohnenblust--Hille inequality. In this note we obtain upper bounds for opposite side, i.e., the constants when $2m\le p\le 2m^3-4m^2+2m.$ For these values of $p$ our result improves previous estimates from 2014 of Araujo \textit{et al}. for all $m\ge 3.$

References in corpus (1)

• On the constants of the Bohnenblust-Hille inequality and Hardy--Littlewood inequalities