Moment inequalities connected with accompanying Poisson laws in Abelian groups (Q1415132)

Let \(X_i\) be independent random variables with respective distributions \(P_i\) taking values in a measurable Abelian group \(G\), \(S_n=X_1+\cdots +X_n\). The author obtains exact moment inequalities for some measurable functions of \(S_n\) via the analogous moments of the accompanying Poisson law, the generalized Poisson distribution with the Lévy measure \(\mu =P_1+\cdots +P_n\). The case where \(G\) is a Banach space is considered in detail. As an application, estimates of the expectation of some functionals of empirical processes are given.