Exact regularity of $\bar{\partial}$ on pseudoconvex domains in $\mathbb{C}^2$

Abstract

We show there is a solution operator to $\bar{\partial}$ which is bounded as a map $W^{s}_{(0,1)}(\Omega)\cap\mbox{ker }\bar{\partial}\rightarrow W^{s}(\Omega)$ for all $s\ge 0$.