On compactness of the dbar-Neumann problem and Hankel operators

Abstract

Let \D=\D_1\setminus \Dc_2, where \D_1 and \D_2 are two smooth bounded pseudoconvex domains in \C^n, n\geq 3, such that \Dc_2\subset \D_1. Assume that the \dbar-Neumann operator of \D_1 is compact and the interior of the Levi-flat points in the boundary of \D_2 is not empty (in the relative topology). Then we show that the Hankel operator on \D with symbol \phi, H^{\D}_{\phi}, is compact for every \phi\in C(\Dc) but the \dbar-Neumann operator on \D is not compact.Comment: 8 pages, to appear in Proc. Amer. Math. So