Toeplitz operators on the Bergman space of planar domains with essentially radial symbols (Q638070)

Summary: We study the problem of the boundedness and compactness of the Toeplitz operator \(T_{\phi}\) when \(\phi \in L^2(\Omega)\) and \(\Omega\) is a planar domain. We find a necessary and sufficient condition while imposing a condition that generalizes the notion of radial symbol on the disk. We also analyze the relationship between the boundary behavior of the Berezin transform and the compactness of \(T_{\phi}\).