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

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