Bounded and compact operators on the Bergman space La1 in the unit ball of Cn

AbstractLet μ be a complex Borel measure on the unit ball of Cn and α>−1. We characterize the measures μ for which the Toeplitz operator Tμα is bounded or compact on the Bergman space La1(Bn,(1−|z|2)αdν), where dν is the normalized Lebesgue measure on the unit ball of Cn. Our results also include the case of more general operators in La1(Bn,dν). These results extend to several dimensions the results of Agbor, Békollé and Tchoundja (2011) [2] and Wu, Zhao and Zorborska (2006) [11]