Polynomial and multilinear Hardy--Littlewood inequalities: analytical and numerical approaches

Abstract

We investigate the growth of the polynomial and multilinear Hardy--Littlewood inequalities. Analytical and numerical approaches are performed and, in particular, among other results, we show that a simple application of the best known constants of the Clarkson inequality improves a recent result of Araujo et al. We also obtain the optimal constants of the generalized Hardy--Littlewood inequality in some special cases.

The title was modified. The computer-assisted part of the previous version is now fixed and this new version has a new section which corresponds to the arXiv submission 1504.04207. The arXiv submission 1504.04207 does not exist as an independent paper and now is part of the present paper

References in corpus (3)

• On the upper bounds for the constants of the Hardy-Littlewood inequality
• Optimal exponents for Hardy--Littlewood inequalities for $m$-linear operators
• Sharp generalizations of the multilinear Bohnenblust--Hille inequality

Cited by in corpus (1)

• New lower bounds for the constants in the real polynomial Hardy--Littlewood inequality