Hardy's inequalities with non-doubling weights and sharp remainders

2020/12/16 by Toshio Horiuchi, Horiuchi, Toshio · 1 citation
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2012.08766

openalex publication_date 2020/12/16 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In the present paper we shall establish n-dimensional Hardy's inequalities with non-doubling weight functions of the distance to the boundary, where the boundary is a C² class bounded domain of R^N. This work is essentially based on one dimensional weighted Hardy's inequalities with one-sided boundary condition and sharp remainders. As weights we admit rather general ones that may vanish or blow up in infinite order such as e^-1/t or e^1/t at t=0 in one dimensional case.

Cited by

• On general Caffarelli-Kohn-Nirenberg type inequalities involving non-doubling weights in the case of p=1

Related

• One dimensional Weighted Hardy's Inequalities and application
• Generalized weighted Hardy's inequalities with compact perturbations
• Noncritical Weighted Hardy's Inequalities with compact perturbations
• L^p Hardy inequality on C^1,γ domains
• Hardy-Sobolev inequalities with distance to the boundary weight functions