  We consider the spatially homogeneous Boltzmann equation for regularized soft
potentials and Grad's angular cutoff. We prove that uniform (in time) bounds in
$L^1 ((1 + |v|^s)dv)$ and $H^k$ norms, $s, k \ge 0$ hold for its solution. The
proof is based on the mixture of estimates of polynomial growth in time of
those norms together with the quantitative results of relaxation to equilibrium
in $L^1$ obtained by the so-called "entropy-entropy production" method in the
context of dissipative systems with slowly growing a priori bounds (see
reference [14]).
