Sharp inequalities involving multiplicative chaos sums

Abstract

The present note is an addition to the author’s recent paper [44], concerning general multiplicative systems of random variables. Using some lemmas and the methodology of [13], we obtain a general extremal inequality, with corollaries involving Rademacher chaos sums and those analogues for multiplicative systems. In particular we prove that a system of functions generated by bounded products of a multiplicative system is a convergence system.