Weighted Hardy Inequalities for Increasing Functions

Abstract

Abstract The purpose of this paper is to characterize the weight functions for which the Hardy operator , with non-decreasing function ƒ, is bounded between various weighted L p -spaces for a wide range of indices. Our characterizations complement for the most part those of E. T. Sawyer [11] and V. D. Stepanov [15] for the Hardy operator of non-increasing function.