Open Access
Translator Disclaimer
2015 Musielak--Orlicz Spaces that are Isomorphic to Subspaces of $L_1$
Joscha Prochno
Ann. Funct. Anal. 6(1): 84-94 (2015). DOI: 10.15352/afa/06-1-7

Abstract

We prove that $\frac{1}{n!}\sum_{\pi\in\mathfrak{S}_n} \left( \sum\limits_{i=1}^n | {x_ia_{i,\pi(i)}}^2 \right)^{\frac{1}{2}}$ is equivalent to a Musielak--Orlicz norm $\|{x}\|_{\Sigma M_i}$. 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 $L_1$.

Citation

Download Citation

Joscha Prochno. "Musielak--Orlicz Spaces that are Isomorphic to Subspaces of $L_1$." Ann. Funct. Anal. 6 (1) 84 - 94, 2015. https://doi.org/10.15352/afa/06-1-7

Information

Published: 2015
First available in Project Euclid: 19 December 2014

zbMATH: 1331.46014
MathSciNet: MR3297789
Digital Object Identifier: 10.15352/afa/06-1-7

Subjects:
Primary: 46B03
Secondary: 05A20, 46B09, 46B45

Rights: Copyright © 2015 Tusi Mathematical Research Group

JOURNAL ARTICLE
11 PAGES


SHARE
Vol.6 • No. 1 • 2015
Back to Top