Two limits on Hardy and Sobolev inequalities

2019/11/11 by Megumi Sano, Sano, Megumi
Mathematics · #Advanced Harmonic Analysis Research #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1911.04105

openalex publication_date 2019/11/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

It is known that classical Hardy and Sobolev inequalities hold when the exponent p and the dimension N satisfy p < N < ∞. In this note, we consider two limits of Hardy and Sobolev inequalities as p \nearrow N and N \nearrow ∞ in some sense.

Citations

• Logarithmic Sobolev Inequalities

Related

• Remarks on a limiting case of Hardy type inequalities
• On the best constant of Hardy-Sobolev Inequalities
• Sobolev inequalities for the Hardy-Schrödinger operator: Extremals and critical dimensions
• Bilateral Hardy-type inequalities
• Hardy Inequalities in General Domains