Toeplitz Operators on the Bergman Space of Planar Domains with Essentially Radial Symbols

We study the problem of the boundedness and compactness of when ∈2(Ω) and Ω 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 .