  The purpose of this paper is to establish sufficient conditions for closed
range estimates on $(0,q)$-forms, for some fixed $q$, $1 \leq q \leq n-1$, for
$\bar\partial_b$ in both $L^2$ and $L^2$-Sobolev spaces in embedded, not
necessarily pseudoconvex CR manifolds of hypersurface type. The condition,
named weak $Y(q)$, is both more general than previously established sufficient
conditions and easier to check. Applications of our estimates include estimates
for the Szeg\"o projection as well as an argument that the harmonic forms have
the same regularity as the complex Green operator. We use a microlocal argument
and carefully construct a norm that is well-suited for a microlocal
decomposition of form. We do not require that the CR manifold is the boundary
of a domain. Finally, we provide an example that demonstrates that weak $Y(q)$
is an easier condition to verify than earlier, less general conditions.
