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 HfHg*. where f and g are square integrable on the unit dish, and for the mixed Haplitz products HfTg and TgHf*, where f and g are square integrable on the unit disk and g is analytic. (C) 1999 Academic Press.