T. Figiel et al., EXTREMAL PROPERTIES OF RADEMACHER FUNCTIONS WITH APPLICATIONS TO THE KHINTCHINE AND ROSENTHAL INEQUALITIES, Transactions of the American Mathematical Society, 349(3), 1997, pp. 997-1027
The best constant and the extreme cases in an inequality of H.P. Rosen
thal, relating the p moment of a sum of independent symmetric random v
ariables to that of the p and 2 moments of the individual variables, a
re computed in the range 2 < p less than or equal to 4. This complemen
ts the work of Utev who has done the same for p > 4. The qualitative n
ature of the extreme cases turns out to be different for p < 4 than fo
r p > 4. The method developed yields results in some more general and
other related moment inequalities.