Sharp Caffarelli–Kohn–Nirenberg inequalities on stratified Lie groups

Abstract

In this paper, we prove a family of sharp Caffarelli-Kohn-Nirenberg inequalities on stratified Lie groups. Our result sharpens the inequalities obtained recently by Ruzhansky, Suragan and Yessirkegenov [22], and extend the classical Caffarelli-Kohn-Nirenberg inequalities to a new class of exponents (negative or smaller than 1) which we believe to be new in literature. Finally, we generalize our result to the more general setting of homogeneous groups with any homogeneous quasi-norm.

The sharp second order Caffareli-Kohn-Nirenberg inequality and stability estimates for the sharp second order uncertainty principle

“…In [49], Xia extends the inequality (1.1) and obtain the following inequality The inequality (1.2) is extended to the Riemannian manifolds in [41], the Finsler manifolds in [31] and the stratified Lie groups in [38].…”