Optimal Hölder Regularity of Solution Operator to the $\bar{\partial }$-equation on Product Domains

Abstract

This note seeks to prove the existence of a canonical solution operator to the $\bar{\partial }$-equation that preserves Hölder regularity on product domains. It is a well known fact that such solution operators do not in general gain Hölder regularity, and as such, our solution operator is optimal in this regard.

This paper has been withdrawn due to a gap in the main theorem