A note on a two-parameter family of operators $\mathcal{A}^{b,c}$ on weighted Bergman spaces

In this article, we prove that the two-parameter family of operators ${\mathcal A}^{b,c}$ is bounded on the weighted Bergman spaces $B_{\alpha+c-1}^p$ if $\alpha+2<p$ and unbounded if $\alpha+2=p$.