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arXiv · 2009.13391

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

Sonmez Sahutoglu·Yunus E. Zeytuncu
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Abstract

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 $L^2_{(0,1)}(\Omega)$ then the embedding operator $\mathcal{J}:Dom(\overline{\partial})\cap Dom(\overline{\partial}^*) \to L^2_{(0,1)}(\Omega)$ is $L^p$-regular for all $2\leq p<\infty$.

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Sonmez Sahutoglu, Yunus E. Zeytuncu. 2020-09-28. On compactness and $L^p$-regularity in the $\overline{\partial}$-Neumann problem. https://doi.org/10.1112/blms.12502

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