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arXiv · 1204.6030

Musielak-Orlicz Spaces that are Isomorphic to Subspaces of L_1

Joscha Prochno
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Abstract

In this note we prove that $\frac{1}{n!} \sum_π (\sum_{i=1}^n |x_i a_{i,π(i)} |^2)^{1/2}$ is equivalent to a Musielak-Orlicz norm $\norm{x}_{\sum M_i}$. We also obtain the inverse 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.

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Joscha Prochno. 2013-05-07. Musielak-Orlicz Spaces that are Isomorphic to Subspaces of L_1. https://arxiv.org/abs/1204.6030

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