On compactness and $L^p$-regularity in the $\overline{\partial }$-Neumann problem

Sonmez Sahutoglu, Yunus E. Zeytuncu

Let $\Omega$ be a $C^4$-smooth bounded pseudoconvex domain in ${\mathbb{C}}^2$. We show that if the $\overline{\partial }$-Neumann operator $N_1$ is compact on $L_{(0,1)}^2(\Omega )$ then the em…