Regularity of dbar on worm domains

Abstract

A solution operator to the $\bar{\partial}$-equation is constructed on unbounded worm domains, $D_{\beta}$. Regularity estimates are proven showing the operator preserves regularity of the data. The operator may be viewed as a continuous mapping among appropriate subpaces of $W^s(D_{\beta})$, which depend on a rotational invariance of the domains.