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 re gularizing properties of the collision gain term in the first equation of t he Boltzmann hierarchy. Some corollaries of the main results of this paper are given to improve the previous results on the regularity of the gain ter m in the Boltzmann equation. An extension of a new fundamental result conce rning separated variable kernels is also given to some general kernels. (C) 1998 Academic Press.