On the embedding of 2-concave Orlicz spaces into $L^1$

Abstract

In [K--S 1] it was shown that $$\underset{\pi }{\to }\text{Ave}(\sum _{i=1}^n|x_i{a}_{\pi (i)}{|}^2{)}^{\frac{1}{2}}$$ is equivalent to an Orlicz norm whose Orlicz function is 2-concave. Here we give a formula for the sequence $a_1,a_2,....,a_n$ so that the above expression is equivalent to a given Orlicz norm.

Cited by in corpus (1)

• An Inversion Formula for Orlicz Norms and Sequences of Random Variables