Products of Toeplitz operators on the harmonic Bergman space

Dong, Xing-Tang; Zhou, Ze-Hua

doi:10.1090/S0002-9939-09-10204-6

Products of Toeplitz operators on the harmonic Bergman space
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by Xing-Tang Dong and Ze-Hua Zhou PDF

Proc. Amer. Math. Soc. 138 (2010), 1765-1773 Request permission

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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