The multilinear Hardy-Littlewood inequalities provide estimates for the sum of the coefficients of multilinear forms T∶ℓp1n× ⋯ × ℓpmn→ R( or C) when 1/p1× ⋯ × 1/pm<1. In this paper we investigate the critical and super-critical cases; i.e., when1/p1× ⋯ × 1/pm≥1
