An Integral Version of Hardy's Inequality

Abstract

In this note we present a version of Hardy's inequality on a measure space $(X,\mu )$ endowed with a measurable function $N:X\to \mathbb{R}$ which replaces the absolute value on $\mathbb{R}$ or ${\mathbb{R}}^n$, and, more generally, the distance function from a given point when $X$ is a metric space.

12 pages, no figures