Hardy-Littlewood-Sobolev and Stein-Weiss inequalities on homogeneous Lie groups

2018/10/26 by Kassymov, Aidyn, Ruzhansky, Michael, Suragan, Durvudkhan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1810.11439

Abstract

In this note we prove the Stein-Weiss inequality on general homogeneous Lie groups. The obtained results extend previously known inequalities. Special properties of homogeneous norms play a key role in our proofs. Also, we give a simple proof of the Hardy-Littlewood-Sobolev inequality on general homogeneous Lie groups.

Related

• Reverse Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev and Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups
• A survey of Hardy type inequalities on homogeneous groups
• All conditions for Stein-Weiss inequalities are necessary
• Euler semigroup, Hardy-Sobolev and Gagliardo-Nirenberg type inequalities on homogeneous groups
• Stein-Weiss-Adams inequality on Morrey spaces