Zhu's reciprocal conjecture for weighted Bergman spaces

Let $\mathbb{B}_n$ denote the unit ball, and let $A^p_\alpha$ be the weighted Bergman space on $\mathbb{B}_n$, where $0<p<\infty$ and $\alpha$ is real. Zhu's reciprocal conjecture. If $f\in A^p_\alpha$ and there exists a constant $c>0$ such that

$$|f(z)|\geq c$$

for all $z\in\mathbb{B}_n$, then $1/f\in A^p_\alpha$. This reciprocal problem asks when a function in a weighted Bergman space remains in that space after inversion under a uniform lower bound; the source identifies the intermediate range of $\alpha$ as difficult. The conjecture is attributed to K. H. Zhu.