Super-critical Hardy--Littlewood inequalities for multilinear forms

2020/02/20 by Nunez-Alarcon, D., Paulino, D., Pellegrino, D.
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2002.10239

Abstract

The multilinear Hardy--Littlewood inequalities provide estimates for the sum of the coefficients of multilinear forms T:ℓ_p₁ⁿ×⋯ ×ℓ_p_mⁿ→ℝ (or ℂ) when 1/p₁+⋯+1/p_m<1. In this paper we investigate the critical and super-critical cases; i.e., when 1/p₁+⋯+1/p_m≥1.

Related

• Critical Hardy--Littlewood inequality for multilinear forms
• Universal bounds for the Hardy--Littlewood inequalities on multilinear\n forms
• Summability of multilinear forms on classical sequence spaces
• A short communication on the constants of the multilinear Hardy--Littlewood inequality
• Optimal Hardy-Littlewood type inequalities for polynomials and multilinear operators