Formulas for approximate solutions of the $\partial \bar{\partial }$-equation in a strictly pseudoconvex domain

Abstract

Let $D$ be a bounded strictly pseudoconvex domain in ${\mathbb{C}}^n$. We construct approximative solution formulas for the equation $i\partial \bar{\partial }u=\theta$, $\theta$ being an exact (1,1 )-form in $D$. We show that our formulas give simple proofs of known estimates and indicate further applications.