A Direct Method for the Regularity of the Gain Term in the Boltzmann Equation

This paper presents an essentially simple and direct method to prove the regularizing properties of the collision gain term in the first equation of the Boltzmann hierarchy. Some corollaries of the main results of this paper are given to improve the previous results on the regularity of the gain term in the Boltzmann equation. An extension of a new fundamental result concerning separated variable kernels is also given to some general kernels