  We reduce the problem of constructing a linear solution operator to the
$\bar{\partial}$-equation on smoothly bounded weakly pseudoconvex domains,
$\Omega$, in $\mathbb{C}^2$ to the problem of the boundary
$\bar{\partial}_b$-equation. We show there is a solution operator to
$\bar{\partial}$ which is bounded as a map $W^{s}_{(0,1)}(\Omega)\cap{ker}
\bar{\partial} \rightarrow W^{s}(\Omega)$ for all $s\ge 0$ if there is a
corresponding solution operator to the $\bar{\partial}_b$-problem with
analogous regularity properties.
