An Integral Version of Hardy's Inequality

2023/02/23 by Mattia Calzi, Calzi, Mattia
Mathematics · #Advanced Banach Space Theory #Advanced Harmonic Analysis Research #FOS: Mathematics #Functional Analysis (math.FA) #Mathematical and Theoretical Analysis

paper · pdf · doi:10.48550/arxiv.2302.12300

openalex publication_date 2023/02/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we present a version of Hardy's inequality on a measure space (X,μ) endowed with a measurable function N\colon X→ \mathbb R which replaces the absolute value on \mathbb R or \mathbb Rⁿ, and, more generally, the distance function from a given point when X is a metric space.

Related

• Reverse integral Hardy inequality on metric measure spaces
• Hardy inequalities on metric measure spaces, III: The case q≤ p<0 and applications
• Bilinear Hardy inequalities on metric measure spaces
• Hardy inequalities on metric measure spaces, IV: The case p=1
• Hardy's inequality and curvature