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arXiv · 1007.0775

The complex Green operator on CR-submanifolds of $\mathbb{C}^{n}$ of hypersurface type: compactness

Emil J. Straube
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Abstract

We establish compactness estimates for $\overline{\partial}_{b}$ on a compact pseudoconvex CR-submanifold of $\mathbb{C}^{n}$ of hypersurface type that satisfies property(P). When the submanifold is orientable, these estimates were proved by A.~Raich via microlocal methods. Our proof deduces the estimates from (a slight extension, when $q>1$, of) those known on hypersurfaces via the fact that locally, CR-submanifolds of hypersurface type are CR-equivalent to a hypersurface. The relationship between two potential theoretic conditions is also clarified.

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Emil J. Straube. 2010-08-09. The complex Green operator on CR-submanifolds of $\mathbb{C}^{n}$ of hypersurface type: compactness. https://arxiv.org/abs/1007.0775

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