  This paper deals with the derivation of some \'a priori estimates for the
homogeneous Landau equation with soft potentials. Using the coercivity of the
Landau operator for soft potentials, we prove a global estimate of weak
solutions in $L^2$ space without any smallness assumption on the initial data
for $ -2 < \gamma <0$. For the stronger case $ -3 \leq \gamma \leq -2$, which
covers in particular the Coulomb case, we get such a global estimate, but in
some weighted $L^2$ space and under a smallness assumption on initial data.
