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

TL;DR

This paper establishes reverse versions of several fundamental inequalities, including Stein-Weiss, Hardy-Littlewood-Sobolev, Hardy, Sobolev, and Caffarelli-Kohn-Nirenberg, on homogeneous Lie groups, extending classical results to a broader setting.

Contribution

It introduces reverse inequalities on homogeneous groups, broadening the scope of classical inequalities in harmonic analysis and PDEs.

Findings

Proved reverse Stein-Weiss inequality on homogeneous groups

Extended reverse Hardy and Sobolev inequalities to this setting

Demonstrated the role of homogeneous norms and reverse Hardy inequality

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.