Abstract
The paper is devoted to the study of Toeplitz operators with separately quasihomogeneous symbols on the Bergman space of the polydisk.First,we obtain necessary and sufficient conditions for the product of two Toeplitz operators with separately quasihomogeneous symbols to be a Toeplitz operator.Next,we provide a decomposition of L2(Dn,dV).Then we use this to show that the zero product of two Toeplitz operators has only a trivial solution if one of the symbols is separately quasihomogeneous and the other is arbitrary.Also,the corresponding commuting problem of Toeplitz operators is studied.
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