Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups

2019/11/30 by Aidyn Kassymov, Michael Ruzhansky, Kassymov, Aidyn +3
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.1912.01460

openalex publication_date 2019/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note we prove the reverse Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms and the reverse integral Hardy inequality play key roles in our proofs. Also, we show reverse Hardy, Hardy-Littlewood-Sobolev, Lp-Sobolev and Lp-Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups.

Related

• Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie\n groups
• Euler semigroup, Hardy-Sobolev and Gagliardo-Nirenberg type inequalities on homogeneous groups
• A survey of Hardy type inequalities on homogeneous groups
• L^p-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups
• All conditions for Stein-Weiss inequalities are necessary