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

Let mu be a complex Borel measure on the unit ball of C-n and alpha > -1. We characterize the measures mu for which the Toeplitz operator T-mu(alpha) is bounded or compact on the Bergman space L-a(1)(B-n, (1 - |z|)(2))(alpha) dv), where dv 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, dv). These results extend to several dimensions the results of Agbor, Bekolle and Tchoundja (2011)[2] and Wu, Zhao and Zorborska (2006)[1]. (C) 2011 Elsevier Inc. All rights reserved.