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arXiv · 1510.00367

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

Daniel Pellegrino
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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 $2m\leq p\leq2m^{3}-4m^{2}+2m.$ For these values of $p$ our result improves previous estimates from 2014 of Araujo \textit{et al}. for all $m\geq3.$

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Daniel Pellegrino. 2015-10-01. A short communication on the constants of the multilinear Hardy--Littlewood inequality. https://arxiv.org/abs/1510.00367

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