  In this paper we prove sharp weighted Hardy-type inequalities on Carnot
groups with the homogeneous norm $N=u^{1/(2-Q)}$ associated to Folland's
fundamental solution $u$ for the sub-Laplacian $\Delta_{\mathbb{G}}$. We also
prove uncertainty principle, Caffarelli-Kohn-Nirenberg and Rellich inequalities
on Carnot groups.
