| Toeplitz Operators with Quasihomogeneous Symbols on the Dirichlet Space of ${\mathbb{B}}_n$ |
| Received:July 27, 2013 Revised:October 12, 2013 |
| Key Words:
Dirichlet space unit ball Toeplitz operators quasihomogeneous symbols.
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant No.11271059). |
| Author Name | Affiliation | | Hongzhao LIN | Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China
Department of Computer and information, Fujian Agriculture and Forestry University, Fujian 350002, P. R. China | | Bo ZHANG | Department of Science, Dalian Ocean University, Liaoning 116023, P. R. China | | Yufeng LU | Department of Mathematics, Dalian University of Technology, Liaoning 116024, P. R. China |
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| Abstract: |
| In this paper, we study some algebraic properties of Toeplitz operators with quasihomogeneous symbols on the Dirichlet space of the unit ball ${\mathbb{B}}_n$. First, we describe commutators of a radial Toeplitz operator and characterize commuting Toeplitz operators with quasihomogeneous symbols. Then we show that finite rank product of such operators only happens in the trivial case. Finally, some necessary and sufficient conditions are given for the product of two quasihomogeneous Toeplitz operators to be a quasihomogeneous Toeplitz operator. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2013.06.008 |
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