  We establish global hypoelliptic estimates for linear Landau-type operators.
Linear Landau-type equations are a class of inhomogeneous kinetic equations
with anisotropic diffusion whose study is motivated by the linearization of the
Landau equation near the Maxwellian distribution. By introducing a microlocal
method by multiplier which can be adapted to various hypoelliptic kinetic
equations, we establish for linear Landau-type operators optimal global
hypoelliptic estimates with loss of 4/3 derivatives in a Sobolev scale which is
exactly related to the anisotropy of the diffusion.
