Abstract We characterize the boundedness and compactness of Toeplitz operators T a with radial symbols a in weighted H ∞ -spaces H v ∞ on the open unit disc of the complex plane. The weights v are also assumed radial and to satisfy the condition (B) introduced by the second named author. The main technique uses Taylor coefficient multipliers, and the results are first proved for them. We formulate a related sufficient condition for the boundedness and compactness of Toeplitz operators in reflexive weighted Bergman spaces on the disc. We also construct a bounded harmonic symbol f such that T f is not bounded in H v ∞ for any v satisfying mild assumptions. As a corollary, the Bergman projection is never bounded with respect to the corresponding weighted sup-norms. However, we also show that, for normal weights v, all Toeplitz operators with a trigonometric polynomial as the symbol are bounded on H v ∞ .

中文翻译：

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加权H∞空间中托普利兹算子的有界性和紧性

摘要 我们在复平面的开单位圆盘上用加权H ∞ -空间H v ∞ 刻画了托普利兹算子T a 的有界性和紧致性。权重 v 也被假定为径向并满足由第二名作者引入的条件 (B)。主要技术使用泰勒系数乘法器，并首先对其结果进行证明。我们为圆盘上自反加权伯格曼空间中托普利兹算子的有界性和紧致性制定了相关的充分条件。我们还构造了一个有界调和符号 f，使得对于满足温和假设的任何 v，T f 不受 H v ∞ 的限制。作为推论，Bergman 投影对于相应的加权 sup-norms 永远不会有界。然而，我们还表明，对于正常权重 v，