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

We investigate the constants of the polynomial and multilinear Hardy-Littlewood inequalities. 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. In a final section, as an independent appendix, we present some computer-aided estimates for the lower bounds of the multilinear Hardy-Littlewood inequalities.