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

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.

to appear in NoDEA

References in corpus (3)

• Hardy Type Inequalities Related to Degenerate Elliptic Differential Operators
• Caffarelli-Kohn-Nirenberg and Sobolev type inequalities on stratified Lie groups
• Extended Caffarelli-Kohn-Nirenberg inequalities, and remainders, stability, and superweights for $L^p$-weighted Hardy inequalities

Cited by in corpus (1)

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