  We explicitly construct a finite number of discrete components in the
restriction of complementary series representations of rank one semisimple
groups $G$ to rank one subgroups $G_1$. For this we use the realizations of
complementary series representations of $G$ and $G_1$ on Sobolev spaces on the
nilpotent radicals $N$ and $N_1$ of the minimal parabolics in $G$ and $G_1$,
respectively. The groups $N$ and $N_1$ are of H-type and we construct
explicitly invariant differential operators between $N$ and $N_1$. These
operators induce the projections onto the discrete components. Our construction
of the invariant differential operators is carried out uniformly in the
framework of H-type groups and also works for those H-type groups which do not
occur as nilpotent radical of a parabolic subgroup in a semisimple group.
