On compactness and $L^p$-regularity in the $\overline{\partial}$-Neumann problem
Sahutoglu, Sonmez; Zeytuncu, Yunus E.;
On compactness and $L^p$-regularity in the $\overline{\partial}$-Neumann problem
Let $Ω$ 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 $L^2_{(0,1)}(Ω)$ then the embedding operator $\mathcal{J}:Dom(\overline{\partial})\cap Dom(\overline{\partial}^*) \to L^2_{(0,1)}(Ω)$ is $L^p$-regular for all $2\leq p<\infty$.
Minor changes. To appear in Bull. Lond. Math. Soc
32W05, Mathematics - Complex Variables, FOS: Mathematics, Complex Variables (math.CV)
32W05, Mathematics - Complex Variables, FOS: Mathematics, Complex Variables (math.CV)
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