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

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.