SUFFICIENT CONDITION FOR COMPACTNESS OF THE partial derivative-NEUMANN OPERATOR USING THE LEVI CORE

On a smooth, bounded pseudoconvex domain omega in Cn, to verify that Catlin's Property (P) holds for b omega, it suffices to check that it holds on the set of D'Angelo infinite type boundary points. In this note, we consider the support of the Levi core, SC(N), a subset of the infinite type points, and show that Property (P) holds for b omega if and only if it holds for SC(N). Consequently, if Property (P) holds on SC(N), then the partial differential -Neumann operator N1 is compact on omega.