Compact Hankel operators on generalized Bergman spaces of the polydisc

We show that for $f$ a continuous function on the closed polydisc $\overline{{\mathbb{D}}^n}$ with $n\ge 2$, the Hankel operator $H_f$ is compact on the Bergman space of ${\mathbb{D}}^n$ if and only if there is a decomposition $f=h+g$, where $h$ is in the ball algebra and $g$ vanishes on the boundary of the polydisc.