Abstract We obtain complete characterizations in terms of Carleson measures for bounded/compact differences of weighted composition operators acting on the standard weighted Bergman spaces over the unit disk. Unlike the known results, we allow the weight functions to be non-holomorphic and unbounded. As a consequence we obtain a compactness characterization for differences of unweighted composition operators acting on the Hardy spaces in terms of Carleson measures and, as a nontrivial application of this, we show that compact differences of composition operators with univalent symbols on the Hardy spaces are exactly the same as those on the weighted Bergman spaces. As another application, we show that an earlier characterization due to Acharyya and Wu for compact differences of weighted composition operators with bounded holomorphic weights does not extend to the case of non-holomorphic weights. We also include some explicit examples related to our results.

中文翻译：

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加权复合算子的差异

摘要 我们根据加权合成算子的有界/紧致差异的 Carleson 测度获得了完整的表征，该差异作用于单位圆盘上的标准加权 Bergman 空间。与已知结果不同，我们允许权重函数是非全纯和无界的。因此，我们根据 Carleson 测度获得了作用在 Hardy 空间上的未加权组合算子的差异的紧致性表征，并且作为这一点的重要应用，我们表明在 Hardy 空间上具有单价符号的复合算子的紧致差异恰好是与加权 Bergman 空间相同。作为另一个应用程序，我们表明，由于 Acharyya 和 Wu 对具有有界全纯权重的加权合成算子的紧凑差异的早期表征不能扩展到非全纯权重的情况。我们还包括一些与我们的结果相关的明确示例。