Propagation of Lp estimates for the spatially homogeneous relativistic Boltzmann equation

In this paper, we prove the propagation of L-p upper bounds for the spatially homogeneous relativistic Boltzmann equation for any 1 < p < infinity. We consider the case of relativistic hard ball with Grad's angular cutoff. Our proof is based on a detailed study of the inter-relationship between the relative momenta, the regularity and the L-p estimates for the gain operator, the development of the relativistic Carleman representation, and several estimates on the relativistic hypersurface E-v'-v(v)*. We also derive a Pythagorean theorem for the relative momenta g(v, v(*)), g(v, v'), and g(v', v(*)), which has a crucial role in the reduction of the momentum singularity. (C) 2020 Elsevier Inc. All rights reserved.