Estimates for the Boltzmann Collision Operator via Radial Symmetry and Fourier Transform

We revisit and extend the L theory of the Boltzmann collision operator by using classical techniques based in the Carleman representation and Fourier analysis. We introduce new ideas based in radial symmetry to greatly simplify existent technical proofs and obtain explicit sharp constants. An additional contribution of this work is the discovery of an unexpected relation between the general Boltzmann collision operator and the Fourier transform of the Maxwellian molecules operator. This relation is used to give a simplified proof of Young’s inequality for the collision operator.