Geodesic
Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk
Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 1-19.

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The reducing subspaces of Toeplitz operators $T_{z_1^N\bar {z}_2^M}$ on Dirichlet type spaces of the ${\mathcal {D}}_\alpha ({\mathbb {D}}^2)$ are described, which extends the results for the corresponding operators on Bergman spaces of the bidisk.
DOI : 10.21136/CMJ.2020.0113-19
Classification : 47B35
Keywords: reducing subspace; Toeplitz operator; Dirichlet type space; bidisk 
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Lin, Hongzhao; Teng, Zhongming. Reducing subspaces of Toeplitz operators on Dirichlet type spaces of the bidisk. Czechoslovak Mathematical Journal, Tome 71 (2021) no. 1, pp. 1-19. doi : 10.21136/CMJ.2020.0113-19. http://geodesic.mathdoc.fr/articles/10.21136/CMJ.2020.0113-19/

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