Wiegerinck's conjecture on Bergman spaces of Stein domains

Let $D$ be a Stein domain in $\mathbb C^n$, and let its Bergman space be the space of holomorphic functions on $D$ that belong to $L^2(D)$ with respect to Lebesgue measure. Wiegerinck's conjecture. The Bergman space of $D$ is either trivial or infinite dimensional. Wiegerinck proved this for domains in $\mathbb C$, while finite-dimensional examples are known in $\mathbb C^2$ outside the Stein setting. Despite substantial work and partial results, the conjecture remains open.