Generalizing the notion of invariant subspaces on the 2-dimensional torus $T^2$, we study the structure of $A_\phi$-invariant subspaces of $L^2(T^2)$. A complete description is given of $A_\phi$-invariant subspaces that satisfy conditions similar to those studied by Mandrekar, Nakazi, and Takahashi.

MSC Classifications:

32A35, 47A15 show english descriptions $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]
Invariant subspaces [See also 47A46] 32A35 - $H^p$-spaces, Nevanlinna spaces [See also 32M15, 42B30, 43A85, 46J15]
47A15 - Invariant subspaces [See also 47A46]

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