The Orlicz inequality for multilinear forms

Abstract

The Orlicz (ℓ2,ℓ1)-mixed inequality states that(∑j1=1n(∑j2=1n|A(ej1,ej2)|)2)12≤2‖A‖ for all bilinear forms A:Kn×Kn→K and all positive integers n, where Kn denotes Rn or Cn endowed with the supremum norm. In this paper we extend this inequality to multilinear forms, with Kn endowed with ℓp norms for all p∈[1,∞].