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

## TL;DR

This paper develops weighted Sobolev estimates for the $ar{ ext{d}}$-Neumann problem on intersections of two strictly pseudoconvex domains in $ ext{C}^2$, advancing understanding of regularity in complex analysis.

## Contribution

It introduces weighted estimates for the $ar{ ext{d}}$-Neumann operator on intersecting pseudoconvex domains, extending regularity results to more complex geometries.

## Key findings

- Weighted Sobolev estimates established for the $ar{ ext{d}}$-Neumann problem.
- Regularity results depend on powers of defining functions of the domains.
- Analysis applies to intersections of two smooth strictly pseudoconvex domains.

## 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.