In this paper we prove that the boundedness and compactness of Toeplitz operator with a BMOα1 symbol on the weighted Bergman space Aα2（Bn） of the unit ball is completely determined by the behavior of its Berezin transform, where ≥ -1 and n 〉 1.
In this paper, we study the commutativity of dual Toeplitz operators on weighted Bergman spaces of the unit ball. We obtain the necessary and sufficient conditions for the commutativity, essential commutativity and essential semi-commutativity of dual Toeplitz operator on the weighted Bergman spaces of the unit ball.
