Bounded Toeplitz products on the weighted Bergman spaces of the unit ball

Let p > 1 and let q denote the number such that (1/p) + (1/q) = 1. We give a necessary condition for the product of Toeplitz operators T f T ¯g to be bounded on the weighted Bergman space of the unit ball Apα (α > −1), where f ∈ Apα and g ∈ Aq α, as well as a sufficient condition for T f T ¯g to be bounded on Apα . We use techniques different from those in [K. Stroethoff, D. Zheng, Bounded Toeplitz products on Bergman spaces of the unit ball, J. Math. Anal. Appl. 325 (2007) 114–129], in which the case p =2 was proved.