Exact Rosenthal-type bounds

It is shown that, for any given p.5, A>0 and B>0, the exact upper bound on E|.Xi|p over all independent zero-mean random variables (r.v..s) X1,.,Xn such that .EX2i=B and .E|Xi|p=A equals cpE|....|p, where (.,c).(0,.)2 is the unique solution to the system of equations cp.=A and c2.=B, and .. is a Poisson r.v. with mean .. In fact, a more general result is obtained, as well as other related ones. As a tool used in the proof, a calculus of variations of moments of infinitely divisible distributions with respect to variations of the Lévy characteristics is developed.