S. Kwapien et al., COMPARISON OF MOMENTS OF SUMS OF INDEPENDENT RANDOM-VARIABLES AND DIFFERENTIAL-INEQUALITIES, Journal of functional analysis, 136(1), 1996, pp. 258-268
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.