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arXiv · 1311.4208

Sobolev estimates for the complex Green operator on CR submanifolds of hypersurface type

Emil J. Straube·Yunus E. Zeytuncu
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Abstract

Let $M$ be a pseudoconvex, oriented, bounded and closed CR submanifold of $\mathbb{C}^{n}$ of hypersurface type. Our main result says that when a certain $1$-form on $M$ is exact on the null space of the Levi form, then the complex Green operator on $M$ satisfies Sobolev estimates. This happens in particular when $M$ admits a set of plurisubharmonic defining functions or when $M$ is strictly pseudoconvex except for the points on a simply connected complex submanifold.

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Emil J. Straube, Yunus E. Zeytuncu. 2013-11-17. Sobolev estimates for the complex Green operator on CR submanifolds of hypersurface type. https://arxiv.org/abs/1311.4208

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