Products of Hankel and Toeplitz Operators on the Bergman Space

We consider the question for which square integrable analytic functions f and g on the unit disk the densely defined products TfTg are bounded on the Bergman space. We prove results analogous to those obtained by the second author [17] for such Toeplitz products on the Hardy space. We furthermore obtain similar results for Hankel products HfH*g, where f and g are square integrable on the unit disk, and for the mixed Haplitz products HfTg and TgH*f, where f and g are square integrable on the unit disk and g is analytic.