Compact Toeplitz operators via the Berezin transform on radial weighted Bergman spaces

Let $ω$ be a radial $\widehat{\mathcal D}$-weight and $u$ be a bounded function on the unit disk $\mathbb D$. We prove that the Toeplitz operator \(T_{ω,u}\) is compact on \(A_ω^2\) if and only if its Berezin transform vanishes at the boundary. Our approach is based on a polynomial frame for $A_ω^2$