Musielak-Orlicz spaces that are isomorphic to subspaces of L1

Prochno, Joscha

Abstract

We prove that 1/n! ∑π∈Gn (∑ni=1 |xiai,π(i)|2)1/2 is equivalent to a Musielak-Orlicz norm ||x||∑Mi. We also provide the converse result, i.e., given the Orlicz functions, we provide a formula for the choice of the matrix that generates the corresponding Musielak-Orlicz norm. As a consequence, we obtain the embedding of 2-concave Musielak-Orlicz spaces into L1.

Citation

Prochno, J. (2015). Musielak-Orlicz spaces that are isomorphic to subspaces of L1. Annals of Functional Analysis, 6(1), 84-94. https://doi.org/10.15352/afa/06-1-7

• Journal Article Type: Article
• Acceptance Date: Jul 15, 2013
• Publication Date: 2015
• Deposit Date: Jun 29, 2018
• Electronic ISSN: 2008-8752
• Publisher: Duke University Press
• Peer Reviewed: Peer Reviewed
• Volume: 6
• Issue: 1
• Pages: 84-94
• DOI: https://doi.org/10.15352/afa/06-1-7
• Keywords: Subspace of L₁; Orlicz space; Musielak--Orlicz space; Combinatorial inequality
• Public URL: https://hull-repository.worktribe.com/output/901030
• Publisher URL: https://projecteuclid.org/euclid.afa/1419001452