Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups

TL;DR

This paper proves sharp Caffarelli-Kohn-Nirenberg and Sobolev inequalities on stratified Lie groups, demonstrating their equivalence to Hardy inequalities in the L^2 case, expanding the understanding of functional inequalities in this setting.

Contribution

It establishes sharp weighted inequalities on stratified Lie groups and shows their equivalence to Hardy inequalities in the L^2 case, extending classical results to a non-commutative setting.

Findings

Sharp Caffarelli-Kohn-Nirenberg inequalities on stratified Lie groups

Weighted L^p-Sobolev inequalities with sharp constants

Equivalence between Sobolev and Hardy inequalities in L^2 case

Abstract

In this short paper, we establish a range of Caffarelli-Kohn-Nirenberg and weighted $L^{p}$-Sobolev type inequalities on stratified Lie groups. All inequalities are obtained with sharp constants. Moreover, the equivalence of the Sobolev type inequality and Hardy inequality is shown in the $L^{2}$-case.