The Optimal Constant in Generalized Hardy's Inequality

TL;DR

This paper determines the exact optimal constant in a generalized form of Hardy's inequality involving two Borel measures, unifying previous continuous and discrete cases.

Contribution

It provides the sharp factor for the two-sided estimates of the optimal constant in a generalized Hardy's inequality with two measures.

Findings

Derived the exact optimal constant for the inequality.

Unified continuous and discrete cases under a general framework.

Enhanced understanding of Hardy's inequality with Borel measures.

Abstract

We obtain the sharp factor of the two-sides estimates of the optimal constant in generalized Hardy's inequality with two general Borel measures on $\mathbb{R}$, which generalizes and unifies the known continuous and discrete cases.