COMPARISON OF MOMENTS OF SUMS OF INDEPENDENT RANDOM-VARIABLES AND DIFFERENTIAL-INEQUALITIES

For S=Sigma X(i) xi(i), where (xi(i)) is a sequence of independent, sy mmetric random variables and (x(i)) is a sequence of vectors in a norm ed space we give two methods of proving inequalities (E parallel to S parallel to(p))(1/p) less than or equal to C-p,C-q (E parallel to S pa rallel to(q))(1/q) with the constants C-p,C-q independent of the seque nce (x(i)). The methods depend on using differential inequalities of p oincare or logarithmic Sobolev type. The obtained constants are usuall y better than the ones obtained by other methods. (C) 1996 Academic Pr ess, Inc.