A unified approach to improved L^p Hardy inequalities with best constants

2003/02/26 by Gerassimos Barbatis, Barbatis, G., Stathis Filippas +3 · 4 citations
Mathematics · #35J20 (Primary) 26D10 #46E35 (Secondary) #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.math/0302326

openalex publication_date 2003/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We present a unified approach to improved L^p Hardy inequalities in \R^N. We consider Hardy potentials that involve either the distance from a point, or the distance from the boundary, or even the intermediate case where distance is taken from a surface of codimension 1

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• Sharp second order inequalities with distance function to the boundary and applications to a p-Biharmonic singular problem
• Littlewood--Paley estimates for pure-jump Dirichlet forms

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