Weighted estimates for the $\bar{\partial }$-Neumann problem on intersections of strictly pseudoconvex domains in ${\mathbb{C}}^2$

Abstract

We obtain weighted estimates for the $\bar{\partial }$-Neumann operator on intersections of two smooth strictly pseudoconvex domains in ${\mathbb{C}}^2$. The regularity estimates are described with the use of Sobolev norms with weights which are powers of the defining functions of the two domains.

54 pages; comments welcome