Abstract. A result of K. Stroethoff and D. Zheng provides on the polydisk a necessary and sufficient condition for the Toeplitz product $T_fT_{\overline g}$ to be bounded on the unweighted Bergman space. We consider the same question on the vector weighted Bergman space of the unit polydisc.

DOI: 10.14232/actasm-012-777-1

AMS Subject Classification (1991): 32A36, 47B35

Keyword(s): Bergman spaces, reproducing kernel, Toeplitz operator

Received May 2, 2012, and in final form August 20, 2014. (Registered under 27/2012.)