On a continuous Gale-Berlekamp switching game.

We propose a continuous version of the classical Gale-Berlekamp switching game. The main results of this paper concern growth estimates for the corresponding optimization problems.

Super-critical Hardy-Littlewood inequalities for multilinear forms.

The multilinear Hardy-Littlewood inequalities provide estimates for the sum of the coefficients of multilinear forms T ∶ ℓ p 1 n × ⋯ × ℓ p m n → R ( or  C ) when 1 / p 1 × ⋯ × 1 / p m < 1 . In this paper we investigate the critical and super-critical cases; i.e.

Bohnenblust-Hille inequalities: analytical and computational aspects.

The Bohnenblust-Hille polynomial and multilinear inequalities were proved in 1931 and the determination of exact values of their constants is still an open and challenging problem, pursued by various authors. The present paper briefly surveys recent attempts to attack/solve this problem; it also presents new results, like connections with classical results of the linear theory of absolutely summing operators, and new perspectives.