Bounded Toeplitz products on the Bergman space of the polydisk

We consider the question for which square integrable analytic functions f and g on the polydisk the densely defined products Tf T¯ g are bounded on the Bergman space. We prove results analogous to those we obtained in the setting of the unit disk [K. Stroethoff, D. Zheng, J. Funct. Anal. 169 (1999) 289–313].  2003 Elsevier Science (USA). All rights reserved