Anisotropic $L^{2}$-weighted Hardy and $L^{2}$-Caffarelli-Kohn-Nirenberg inequalities

Michael Ruzhansky, Durvudkhan Suragan

Published 2016-10-22Version 1

We establish sharp remainder terms of the $L^{2}$-Caffarelli-Kohn-Niren\-berg inequalities on homogeneous groups, yielding the inequalities with best constants. Our methods also give new sharp Caffarelli-Kohn-Nirenberg type inequalities in $\mathbb{R}^{n}$ with arbitrary quasi-norms. We also present explicit examples to illustrate our results for different weights and in abelian cases.