On the generalized Bohnenblust–Hille inequality for real scalars

Abstract

In this paper we obtain new lower and upper estimates for the sharp constants in the generalized Bohnenblust–Hille inequality introduced in Albuquerque et al. (J Funct Anal 266:3726–3740, 2014). We apply these results to find optimal constants in the generalized Bohnenblust–Hille inequality and also to recover the optimal constants of the mixed $$\left( \ell _{1},\ell _{2}\right) $$ -Littlewood inequalities recently obtained in Pellegrino (J Number Theory 160:11–18, 2016) and Pellegrino and Teixeira (Commun Contemp Math, to appear).