The Berezin Transform of Toeplitz Operators on the Weighted Bergman Space

In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Bekolle-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.