$L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous   groups
  We prove $L^{p}$-Caffarelli-Kohn-Nirenberg type inequalities on homogeneous groups, which is one of most general subclasses of nilpotent Lie groups, all with sharp constants. We also discuss some of their consequences. Already in the abelian case of $\mathbb{R}^{n}$ our results provide new insights in view of the arbitrariness of the choice of the not necessarily Euclidean quasi-norm. 
Tohru Ozawa, Michael Ruzhansky, Durvudkhan Suragan
math.FA math.AP