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.

Paper is withdrawn due to error in the proof of Lemma 2.1