An improved one-dimensional Hardy inequality

2022/04/02 by Rupert L. Frank, Frank, Rupert L., Ари Лаптев +3 · 2 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Functional Analysis (math.FA) #Numerical methods in inverse problems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2204.00877

openalex publication_date 2022/04/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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