Abstract
We review the hypoelliptic estimates of Bouchut [1] for the kinetic equation in Sobolev spaces. If f is assumed to have the regularity in velocity, then the result is that f also has the regularity in time and space. We use three types to estimate the regularity of f in time and space: one is the Fourier method, another is the Hörmander’s commutator and the other is the characteristic commutator.