On compactness of the dbar-Neumann problem and Hankel operators

Let $\text{D}={\text{D}}_1\setminus {\text{Dc}}_2$, where ${\text{D}}_1$ and ${\text{D}}_2$ are two smooth bounded pseudoconvex domains in ${\text{C}}^n,n\ge 3,$ such that ${\text{Dc}}_2\subset {\text{D}}_1\mathrm{.}$ Assume that the $\text{dbar}$-Neumann operator of ${\text{D}}_1$ is compact and the interior of the Levi-flat points in the boundary of ${\text{D}}_2$ is not empty (in the relative topology). Then we show that the Hankel operator on $\text{D}$ with symbol $\phi, H^{\D}_{\phi},$iscompactforevery$\phi\in C(\Dc)$butthe$\dbar$-Neumann operator on $\text{D}$ is not compact.