WEIGHTED INEQUALITIES FOR MONOTONE-FUNCTIONS

Weighted norm inequalities are investigated by giving an extension of the Riesz convexity theorem to semi-linear operators on monotone funct ions. Several properties of the classes B(p, n) and C(p, n) introduced by Neugebauer in [13] are given. In particular, we characterize the w eight pairs w, v for which integral-infinity/o f(x)p w(x) dx less-than -or-equal-to C integral-infinity/o (1/x integral-infinity/o f)p v(x) d x, for nondecreasing functions f and 1 less-than-or-equal-to p < infin ity.