Differences of weighted composition operators on the unit polydisk

Let $\varphi_1$ and $\varphi_2$ be holomorphic self-maps of the unit polydisk $\mathbb D^N$, and let $u_1$ and $u_2$ be holomorphic functions on $\mathbb D^N$. We characterize the boundedness and compactness of the difference of weighted composition operators $W_{\varphi_1,u_1}$ and $W_{\varphi_2,u_2}$ from the weighted Bergman space $A^p_{\vec\alpha}$, $0<p<\infty$, $\vec\alpha=(\alpha_1,\dots,\alpha_N)$, $\alpha_j>-1$, $j=1,\dots,N$, to the weighted-type space $H^\infty_v$ of holomorphic functions on the unit polydisk $\mathbb D^N$ in terms of inducing symbols $\varphi_1,\varphi_2,u_1$ and $u_2$.