Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk

Authors: HONGZHAO LIN

Abstract: The reducing subspaces of Toeplitz operators $T_{z_1^N}$(or $T_{z_2^N}$), $T_{z_1^Nz_2^N}$, and $T_{z_1^Nz_2^M}$ on Dirichlet type spaces of the bidisk ${\mathcal{D}}_\alpha({{{\mathbb{D}}}^{2}})$ are described, which extends the results for the corresponding operators on the Bergman space of the bidisk.

Keywords: Reducing subspace, Toeplitz operator, Dirichlet type spaces, bidisk

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