On compactness of Hankel and the $\bar{\mathrm{\partial }}$-Neumann operators on Hartogs domains in ${\mathbb{C}}^2$

We prove that on smooth bounded pseudoconvex Hartogs domains in ${\mathbb{C}}^2$ compactness of the $\bar{\mathrm{\partial }}$-Neumann operator is equivalent to compactness of all Hankel operators with symbols smooth on the closure of the domain.