Weighted modular inequalities for monotone functions

Abstract

Weight characterizations of weighted modular inequalities for operators on the cone of monotone functions are given in terms of composition operators on arbitrary non-negative functions with changes in weights. The results extend to modular inequalities, those corresponding to weighted Lebesgue spaces given by E.T. Sawyer [15]. Application to Hardy and fractional integral operators on monotone functions are given.

Keywords

• Weighted modular inequalities; Orlicz spaces; norms; duality; Hardy type inequalities.