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

AbstractLet 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 TfTg¯ to be bounded on the weighted Bergman space of the unit ball Aαp (α>−1), where f∈Aαp and g∈Aαq, as well as a sufficient condition for TfTg¯ to be bounded on Aαp. 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