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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