[Banach] Abstract of a paper by Soeren Christensen, Joscha Prochno, and Stiene Riemer

This is an announcement for the paper "An inversion formula for Orlicz norms and sequences of random variables" by Soeren Christensen, Joscha Prochno, and Stiene Riemer.

Abstract: Given an Orlicz function $M$, we show which random variables $\xi_i$, $i=1,...,n$ generate the associated Orlicz norm, i.e., which random variables yield $\mathbb{E} \max\limits_{1\leq i \leq n}|x_i\xi_i| \sim \norm{(x_i)_{i=1}^n}_M$. As a corollary we obtain a representation for the distribution function in terms of $M$ and $M'$ which can be easily applied to many examples of interest.

Archive classification: math.FA math.PR

Mathematics Subject Classification: 46B09, 60E15

Remarks: 11 pages

Submitted from: prochno@math.uni-kiel.de

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1204.1242

or

http://arXiv.org/abs/1204.1242