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2015 Musielak--Orlicz Spaces that are Isomorphic to Subspaces of L1
Joscha Prochno
Ann. Funct. Anal. 6(1): 84-94 (2015). DOI: 10.15352/afa/06-1-7

Abstract

We prove that 1n!πSn(i=1n|xiai,π(i)2)12 is equivalent to a Musielak--Orlicz norm xΣMi. 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

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Joscha Prochno. "Musielak--Orlicz Spaces that are Isomorphic to Subspaces of L1." 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

Keywords: combinatorial inequality , Musielak--Orlicz space , Orlicz space , Subspace of

Rights: Copyright © 2015 Tusi Mathematical Research Group

Vol.6 • No. 1 • 2015
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