MOMENT INEQUALITIES FOR SUMS OF CERTAIN INDEPENDENT SYMMETRICAL RANDOM-VARIABLES

This paper gives upper and lower bounds for moments of sums of indepen dent random variables (X-k) which satisfy the condition P(\X\(k) great er than or equal to t) = exp(-N-k(t)), where N-k are concave functions . As a consequence we obtain precise information about the tail probab ilities of linear combinations of independent random variables for whi ch N(t) = \t\(r) for some fixed 0 < r less than or equal to 1. This co mplements work of Gluskin and Kwapien who have done the same for conve x functions N.