Super-critical Hardy-Littlewood inequalities for multilinear forms

Abstract

The multilinear Hardy-Littlewood inequalities provide estimates for the sum of the coefficients of multilinear forms $$T:{\ell }_{p_1}^n\times \cdots \times {\ell }_{p_m}^n\to \mathbb{R}\text{( or}\mathbb{C})$$ when $$1/p_1\times \cdots \times 1/p_m<1$$. In this paper we investigate the critical and super-critical cases; i.e., when$$1/p_1\times \cdots \times 1/p_m\ge 1$$

Key words
Multilinear forms; sequence spaces; inequalities; estimates