Hilbert-Schmidt Hankel operators with harmonic symbols on the Bergman space of strongly pseudoconvex domains in ${\mathbb{C}}^n$

We characterize Hilbert-Schmidt Hankel operators on the Bergman spaces of smooth bounded strongly pseudoconvex domains in ${\mathbb{C}}^n$ for $n\ge 2$. We consider harmonic symbols of class $C^3$ up to the closure of the domain and show $H_{\phi }$ is Hilbert-Schmidt if and only if $\phi$ is holomorphic on the domain.