Embeddings of Orlicz-Lorentz spaces into L₁

2019/02/13 by Prochno, Joscha
#05A20 #46B03 #46B07 #46B20 #Combinatorics (math.CO) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.1902.05043

Abstract

In this article, we show that Orlicz-Lorentz spaces ℓⁿ_M,a, n∈\mathbb N with Orlicz function M and weight sequence a are uniformly isomorphic to subspaces of L₁ if the norm ‖⋅‖_M,a satisfies certain Hardy-type inequalities. This includes the embedding of some Lorentz spaces dⁿ(a,p). Our approach is based on combinatorial averaging techniques and we prove a new result of independent interest that relates suitable averages with Orlicz-Lorentz norms.

Related

• Almost compact embeddings between Orlicz and Lorentz spaces
• Combinatorial Inequalities and Subspaces of L1
• New Results in Analysis of Orlicz-Lorentz spaces
• Non-squareness and local uniform non-squareness properties of Orlicz-Lorentz function spaces endowed with the Orlicz norm
• M-ideal properties in Orlicz-Lorentz spaces