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.