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

Autor: Sahutoglu, Sonmez, Zeytuncu, Yunus E.
Rok vydání: 2020
Předmět:
Zdroj: Bull. Lond. Math. Soc. 53, 2021, no. 5
Druh dokumentu: Working Paper
DOI: 10.1112/blms.12502
Popis: 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 $2\leq p<\infty$.
Comment: Minor changes. To appear in Bull. Lond. Math. Soc
Databáze: arXiv