Super-critical Hardy--Littlewood inequalities for multilinear forms

preprint2020arXivOpen access

Abstract

The multilinear Hardy--Littlewood inequalities provide estimates for the sum of the coefficients of multilinear forms T:ℓp1n×⋯×ℓpmn→RT:\ell_{p_{1}}^{n}\times\cdots \times\ell_{p_{m}}^{n}\rightarrow\mathbb{R} (or C\mathbb{C}) when 1/p1+⋯+1/pm<1.1/p_{1}+\cdots+1/p_{m}<1. In this paper we investigate the critical and super-critical cases; i.e., when 1/p1+⋯+1/pm≥1.1/p_{1}+\cdots+1/p_{m}\geq1.

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