Bounded and compact operators on the Bergman space in the unit ball of

Let μ be a complex Borel measure on the unit ball of C n and α > − 1 . We characterize the measures μ for which the Toeplitz operator T μ α is bounded or compact on the Bergman space L a 1 ( B n , ( 1 − | z | 2 ) α d ν ) , where dν is the normalized Lebesgue measure on the unit ball of C n . Our results also include the case of more general operators in L a 1 ( B n , d ν ) . These results extend to several dimensions the results of Agbor, Békollé and Tchoundja (2011) [2] and Wu, Zhao and Zorborska (2006) [11].