In this paper, we obtain some interesting reproducing kernel estimates and some Carleson properties that play an important role. We characterize the bounded and compact Toeplitz operators on the weighted Bergman spaces with Békollé-Bonami weights in terms of Berezin transforms. Moreover, we estimate the essential norm of them assuming that they are bounded.

中文翻译：

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加权Bergman空间上Toeplitz算子的Berezin变换。

在本文中，我们获得了一些有趣的复制核估计以及一些重要的Carleson属性。我们根据Berezin变换，利用Békollé-Bonami权重来表征加权Bergman空间上的有界和紧致Toeplitz算子。此外，假设它们是有界的，我们估计它们的基本范数。