An improved one-dimensional Hardy inequality
Analysis of PDEs
2022-04-05 v1 Classical Analysis and ODEs
Functional Analysis
Spectral Theory
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 Schr\"odinger operators and we explain the use of Hardy inequalities in that context.
Cite
@article{arxiv.2204.00877,
title = {An improved one-dimensional Hardy inequality},
author = {Rupert L. Frank and Ari Laptev and Timo Weidl},
journal= {arXiv preprint arXiv:2204.00877},
year = {2022}
}
Comments
19 pages; Dedicated, in admiration, to V. Maz'ya on the occasion of his 85th birthday