Bounded Toeplitz Products on the Weighted Bergman Spaces of the Unit Ball
by
Jie Miao
Arkansas State University

Let p > 1 and let q be a number such that (1/p)+(1/q)=1. We give a necessary condition for the product of Toeplitz operators T_fT_{[`g]</sub> to be bounded on the weighted Bergman space of the unit ball A<sup>p</sup><sub>a</sub> (a > -1), where both f ∈ A<sup>p</sup><sub>a</sub> and g ∈ A<sup>q</sup><sub>a</sub>, as well as a sufficient condition for T<sub>f</sub>T<sub>[`g]} to be bounded on A^p_a. Different and simplified techniques are used as compared with the case p=2 when the theorems have been obtained.

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Date received: February 10, 2008