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We discussed the reducing subspaces of Toeplitz operators Tz1Nz2M N≠M on the weighted analytic function spaces of bidisk Hw2(D2). The result shows that if the weight w is of type-I, the structure of reducing subspaces of Tz1Nz2M N≠M on Hw2D2 is very simple.

A Note on Reducing Subspaces of Toeplitz Operator on the Weighted Analytic Function Spaces of the Bidisk Hw2D2