We study algebraic properties of two Toeplitz operators on the weighted Bergman space on the unit disk with harmonic symbols. In particular the product property and commutative property are discussed. Further we apply our results to solve a compactness problem of the product of two Hankel operators on the weighted Bergman space on the unit bidisk.

中文翻译：

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加权Bergman空间上Toeplitz算子的代数性质。

我们用谐波符号研究单位圆盘上加权Bergman空间上两个Toeplitz算子的代数性质。特别讨论了产品性质和交换性质。此外，我们将我们的结果用于解决两个双汉克算子在双磁盘上加权Bergman空间上的乘积的紧性问题。