An improved one-dimensional Hardy inequality

Abstract

We prove a one-dimensional Hardy inequality on the halfline with sharp constant, which improves the classical form of this inequality. As a consequence of this new inequality we can rederive known doubly weighted Hardy inequalities. Our motivation comes from the theory of Schrödinger operators and we explain the use of Hardy inequalities in that context.

19 pages; Dedicated, in admiration, to V. Maz'ya on the occasion of his 85th birthday