On compactness of the dbar-Neumann problem and Hankel operators

Details On compactness of the dbar-Neumann problem and Hankel operators On compactness of the dbar-Neumann problem and Hankel operators

2010-08-25

arxiv.org/abs/1008.4199v2

Proc. Amer. Math. Soc. 140 (2012), no. 1, 153-159

Mathematics

Complex Variables

8 pages, to appear in Proc. Amer. Math. Soc

Scientific paper

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.

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