EXTREMAL PROPERTIES OF RADEMACHER FUNCTIONS WITH APPLICATIONS TO THE KHINTCHINE AND ROSENTHAL INEQUALITIES

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.