For the homogeneous Landau equation, we prove regularization properties of the weak solutions f(v,t) and in particular that it lies in Schwartz space S. This regularity was already obtained by Desvillettes and Villani using weighted Sobolev spaces. However, our proof applies to any suitable weak solution, is more elementary and is based on Littlewood Paley decomposition of the velocity space into annulus parts. Apart from this decomposition, we only use elementary estimates, such as Cauchy-Schwarz or Young's inequalities.