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arXiv · 1405.5849

On the upper bounds for the constants of the Hardy-Littlewood inequality

Gustavo Araujo·Daniel Pellegrino·Diogo D. P. Silva e Silva
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Abstract

The best known upper estimates for the constants of the Hardy--Littlewood inequality for $m$-linear forms on $\ell_{p}$ spaces are of the form $\left(\sqrt{2}\right) ^{m-1}.$ We present better estimates which depend on $p$ and $m$. An interesting consequence is that if $p\geq m^{2}$ then the constants have a subpolynomial growth as $m$ tends to infinity.

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Gustavo Araujo, Daniel Pellegrino, Diogo D. P. Silva e Silva. 2014-05-22. On the upper bounds for the constants of the Hardy-Littlewood inequality. https://doi.org/10.1016/j.jfa.2014.06.014

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