Bulletin of the
Korean Mathematical Society
BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

Article

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Bull. Korean Math. Soc. 2015; 52(5): 1649-1660

Printed September 30, 2015

https://doi.org/10.4134/BKMS.2015.52.5.1649

Copyright © The Korean Mathematical Society.

Reducing subspaces for a class of Toeplitz operators on the Bergman space of the bidisk

Mohammed Albaseer, Yufeng Lu, and Yanyue Shi

Dalian University of Technology, Dalian University of Technology, Ocean University of China

Abstract

In this paper, we completely characterize the nontrivial reducing subspaces of the Toeplitz operator $T_{z_{1}^{N}\overline{z}_{2}^{M}}$ on the Bergman space $A^{2}(\mathbb{D}^2)$, where $N$ and $M$ are positive integers.

Keywords: reducing subspace, Toeplitz operator, polydisk

MSC numbers: Primary 47B35, 46E22