  By using the notion of contraction of Lie groups, we transfer $L^p-L^2$
estimates for joint spectral projectors from the unit complex sphere $\sfera$
in ${{\mathbb{C}}}^{n+1}$ to the reduced Heisenberg group $h^{n}$. In
particular, we deduce some estimates recently obtained by H. Koch and F. Ricci
on $h^n$. As a consequence, we prove, in the spirit of Sogge's work, a discrete
restriction theorem for the sub-Laplacian $L$ on $h^n$.
