  Let M be a smooth, compact, orientable, weakly pseudoconvex manifold of
dimension 3, embedded in C^N (N greater than or equal to 2), of codimension one
or more in C^N, and endowed with the induced CR structure. Assuming that the
tangential Cauchy-Riemann operator \bar\partial_b has closed range in L^2 in
order to rule out the Rossi example, we push regularity up to show
\bar\partial_b has closed range in all Sobolev spaces s for s greater than
zero. We then use the Szeg\"{o} projection to show there is a smooth solution
to the \bar\partial_b problem given smooth data. The results are obtained via
microlocalization by piecing together estimates for functions and (0,1) forms
that hold on different microlocal regions.
