On the constants of the Hardy-Littlewood inequalities
The Bohnenblust-Hille multilinear and polynomial inequalities have been proven to be very useful and powerful in analysis, analytic number theory andRetour ligne automatique
physics. For instance, the subexponentiality of the constants of the polynomial version of the Bohnenblust-Hille inequality (case of complex scalars) was recenly used to obtain the asymptotic growth of the Bohr radius of the n-dimensional polydisk, solving a challenging problem that many researchers have been struggling for several years. The Hardy-Littlewood inequalities are a natural generalization of the Bohnenblust-Hille inequalities to lp spaces. The precise estimates of the constants of the Hardy-Littlewood inequalities are unknown and even its asymptotic growth is a mystery (as it happens with the Bohnenblust-Hille inequality). In this talk we investigate the behavior of the constants of the Hardy-Littlewood inequalities.