Best Possible Results in a Class of Inequalities, II

Abstract

In this paper we shall prove the following theorem. THEOREM. Suppose 1 < p ^ oo, and rp > 1 if p < oo, r > 0 if p = oo. Suppose the matrix A = (α nj!) with α nΛ = w~r (fc ^ n), a nk = 0 (fc > w). Suppose w be the subset of w consisting of nonnegative, monotone sequences. Then {n r~ι } n is maximum, with respect to <, in I where