  In this paper, we study the hypocoercivity for a class of linear kinetic
equations with both transport and degenerately dissipative terms. As concrete
examples, the relaxation operator, Fokker-Planck operator and linearized
Boltzmann operator are considered. By constructing equivalent temporal energy
functionals, time rates of the solution approaching equilibrium in some Hilbert
spaces are obtained when the spatial domain takes the whole space or torus and
when there is a confining force or not. The main tool of the proof is the
macro-micro decomposition combined with Kawashima's argument on dissipation of
the hyperbolic-parabolic system. Finally, a Korn-type inequality with
probability measure is provided to deal with dissipation of momentum
components.
