Toeplitz operators on the bergman space of planar domains with essentially radial symbols

Abstract

We study the problem of the boundedness and compactness of Tφ when φ ∈ L2 (ω) and ωis 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 Tφ. Copyright 2011 Roberto C. Raimondo.