This is an announcement for the paper "A Banach rearrangement norm characterization for tail behavior of measurable functions (random variables)" by E.Ostrovsky and L.Sirota.

Abstract: We construct a Banach rearrangement invariant norm on the measurable space for which the finiteness of this norm for measurable function (random variable) is equivalent to suitable tail (heavy tail and light tail) behavior. We investigate also a conjugate to offered spaces and obtain some embedding theorems. Possible applications: Functional Analysis (for instance, interpolation of operators), Integral Equations, Probability Theory and Statistics (tail estimations for random variables).

Archive classification: math.FA math.PR

Submitted from: leos@post.sce.ac.il

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

http://front.math.ucdavis.edu/1210.1168

or

http://arXiv.org/abs/1210.1168