中文摘要：

给出了Nφ-型商模上符号为ZN的解析Toeplitz算子的约化子空间的完备刻画，然后从超等距膨胀算子理论的角度研究Nφ-型商模上符号为一般有限Blaschke积的解析Toeplitz算子的约化子空间的存在性问题，

英文摘要：

This paper first gives a complete description of the reducing subspaces of the analytic Toeplitz operator with symbol z N on Nφ- type quotient modules on the torus, and then researches the reducible problem of the analytic Toeplitz operator with finite Blaschke product symbol on Nφ from the theory of super - isometric dilatable operators.