Bull. Korean Math. Soc. 2013; 50(2): 687-696
Printed March 31, 2013
https://doi.org/10.4134/BKMS.2013.50.2.687
Copyright © The Korean Mathematical Society.
Yanyue Shi and Yufeng Lu
Ocean University of China, Dalian University of Technology
In this note, we completely characterize the reducing subspaces of $T_{z_1^Nz_2^M}$ on $A_{\alpha}^{2}(D^{2})$ where $\alpha>-1$ and $N,M$ are positive integers with $N\neq M$, and show that the minimal reducing subspaces of $T_{z_1^Nz_2^M}$ on the unweighted Bergman space and on the weighted Bergman space are different.
Keywords: Toeplitz operator, reducing subspace, Bergman space
MSC numbers: Primary 47B35, 47B38
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