  In the paper, we establish the existence of steady boundary layer solution of
Boltzmann equation with specular boundary condition in $L^2_{x,v}\cap
L^\infty_{x,v}$ in half-space. The uniqueness, continuity and exponential decay
of the solution are obtained, and such estimates are important to prove the
Hilbert expansion of Boltzmann equation for half-space problem with specular
boundary condition.
