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

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, -Sobolev and -Caffarelli-Kohn-Nirenberg inequalities on homogeneous groups.