Bohnenblust-Hille inequalities: analytical and computational aspects

Abstract

Abstract 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.

Keywords

• Bohnenblust-Hille inequality
• Hardy-Littlewood inequality
• extreme points
• Banach spaces