A new regularization mechanism for the Boltzmann equation without cut-off

We apply recent results on regularity for general integro-differential equations to derive a priori estimates in H"older spaces for the space homogeneous Boltzmann equation in the non cut-off case. We also show an a priori estimate in $L^{\mathrm{\infty }}$ which applies in the space inhomogeneous case as well, provided that the macroscopic quantities remain bounded.