  We study the regularity of infinitesimal CR automorphisms of abstract CR
structures which possess a certain microlocal extension and show that there are
smooth multipliers, completely determined by the CR structure, such that if $X$
is such an infinitesimal CR automorphism, then $\lambda X$ is smooth for all
multipliers $\lambda$. As an application, we study the regularity of
infinitesimal automorphisms of certain embedded hypersurfaces of infinite type.
