New Lower Bounds for the Constants in the Real Polynomial Hardy–Littlewood Inequality

Abstract

In this short note we obtain new lower bounds for the constants of the real Hardy-Littlewood inequality for m-linear forms on 2 p spaces when p = 2m and for certain values of m. The real and complex cases for the general case n p were recently investigated in [4] and [6]. When n = 2 our results improve the best known estimates for these constants.arXiv:1506.00159v2 [math.FA]

Bohnenblust-Hille inequalities: analytical and computational aspects

“…In view of the analytic difficulties, a computational approach is reasonable alternative. In fact, some attempts in this direction can be seen in and Cavalcante et al (2016), but these approaches are restricted to very particular cases. A recent result of Pellegrino and Teixeira (2017) shows that a particular instance of the Bohnenblust-Hille inequality can be re-written as an algorithm, opening some possibilities for further computational investigations.…”

“…Further generalizations to the anisotropic settings were obtained in Albuquerque et al (2014) and the best known estimates for C K,m,p can be found in Pellegrino (2014, 2017) and Cavalcante et al (2016). The case m < p < 2m was recently explored in Dimant and Sevilla-Peris (2016) and the constants involved were further explored in Albuquerque et al (2017), Nunes (2017), among others.…”