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- W4299291127 abstract "The purpose of this article is to study compactness of the complex Green operator on CR manifolds of hypersurface type. We introduce (CR-P_q), a potential theoretic condition on $(0,q)$-forms that generalizes Catlin's property (P_q) to CR manifolds of arbitrary codimension. We prove that if an embedded CR-manifold of hypersurface type satisfies (CR-P_q) and (CR-P_{n-1-q}) and is of real dimension at least five, then the complex Green operator is a compact operator on the Sobolev spaces $H^s_{0,q}(M)$, if $1leq q leq n-2$ and $sgeq 0$. We use CR-plurisubharmonic functions to build a microlocal norm that controls the totally real direction of the tangent bundle." @default.
- W4299291127 created "2022-10-02" @default.
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- W4299291127 date "2008-10-14" @default.
- W4299291127 modified "2023-09-28" @default.
- W4299291127 title "Compactness of the Complex Green Operator on CR-Manifolds of Hypersurface Type" @default.
- W4299291127 doi "https://doi.org/10.48550/arxiv.0810.2553" @default.
- W4299291127 hasPublicationYear "2008" @default.
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