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

TL;DR

This paper explores the growth of Hardy--Littlewood inequalities for polynomials and multilinear forms, using analytical and numerical methods to improve constants and identify optimal values in specific cases.

Contribution

It introduces improved bounds for the inequalities' constants and determines optimal constants in certain scenarios, advancing understanding of these inequalities.

Findings

Improved constants for Hardy--Littlewood inequalities.

Application of Clarkson inequality enhances previous results.

Determination of optimal constants in specific cases.

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.