  In this article we provide global subelliptic estimates for the linearized
inhomogeneous Boltzmann equation without angular cutoff, and show that some
global gain in the spatial direction is available although the corresponding
operator is not elliptic in this direction. The proof is based on a multiplier
method and the so-called Wick quantization, together with a careful analysis of
the symbolic properties of the Weyl symbol of the Boltzmann collision operator.
