$\overline{\partial }$-Estimates on the product of bounded Lipschitz domain

Abstract

Let $D$ be a bounded domain in the complex plane with Lipschitz boundary. In the paper, we construct an integral solution operator $T[f]$ for any $\overline{\partial }$ closed $(0,1)$-form $f\in L_{(0,1)}^p(D^n)$ solving the Cauchy-Riemain equation $\overline{\partial }u=f$ on the product domains $D^n$ and obtain the $L^p$-estimates for all $1<p\le \infty$.