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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Products of Toeplitz operators on the harmonic Bergman space


Authors: Xing-Tang Dong and Ze-Hua Zhou
Journal: Proc. Amer. Math. Soc. 138 (2010), 1765-1773
MSC (2010): Primary 47B35; Secondary 47B38
Published electronically: December 16, 2009
MathSciNet review: 2587461
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Abstract: In this paper, we first discuss some basic results concerning Toeplitz operators with quasihomogeneous symbols (i.e., symbols being of the form $ e^{ip\theta}\varphi $, where $ \varphi $ is a radial function) on the harmonic Bergman space. Then we determine when the product of two Toeplitz operators with quasihomogeneous symbols is a Toeplitz operator.


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Additional Information

Xing-Tang Dong
Affiliation: Department of Mathematics, Tianjin University, Tianjin 300072, People’s Republic of China
Email: dongxingtang@163.com

Ze-Hua Zhou
Affiliation: Department of Mathematics, Tianjin University, Tianjin 300072, People’s Republic of China
Email: zehuazhou2003@yahoo.com.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-09-10204-6
PII: S 0002-9939(09)10204-6
Keywords: Toeplitz operators, harmonic Bergman space, quasihomogeneous symbols
Received by editor(s): June 30, 2009
Received by editor(s) in revised form: September 7, 2009
Published electronically: December 16, 2009
Additional Notes: The second author was supported in part by the National Natural Science Foundation of China (Grant Nos. 10971153, 10671141).
Communicated by: Nigel J. Kalton
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.