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

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 $p\ge m^2$ then the constants have a subpolynomial growth as $m$ tends to infinity.

References in corpus (2)

• The Bohr radius of the $n$-dimensional polydisk is equivalent to $\sqrt{\frac{\log n}{n}}$
• Sharp generalizations of the multilinear Bohnenblust--Hille inequality

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• The optimal constants of the mixed $\left({\ell }_1,{\ell }_2\right)$-Littlewood inequality
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• On the polynomial Hardy--Littlewood inequality
• The optimal constants for the real Hardy--Littlewood inequality for bilinear forms on $c_0\times {\ell }_p$