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

Sonmez Sahutoglu; Yunus E. Zeytuncu

doi:10.1112/blms.12502

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

Complex Variables 2022-07-28 v2

Authors: 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 $2\leq p<\infty$ .

Keywords

bounded domains lp spaces and inequalities operator theory and elliptic operators

Cite

@article{arxiv.2009.13391,
  title  = {On compactness and $L^p$-regularity in the $\overline{\partial}$-Neumann problem},
  author = {Sonmez Sahutoglu and Yunus E. Zeytuncu},
  journal= {arXiv preprint arXiv:2009.13391},
  year   = {2022}
}

Comments

Minor changes. To appear in Bull. Lond. Math. Soc

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