Bounded Toeplitz products on weighted Bergman spaces

We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products T-f T-g are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unweighted Bergman space [17]. We will furthermore completely describe when the Toephtz; product T-f T-g is invertible or Fredholm and prove results generalizing those we obtained for the unweighted Bergman space in [18].