The paper is devoted to weighted estimates for operators of fractional integration of variable order of Bergman type in generalized variable Hölder spaces of holomorphic functions on the unit disc \( {\mathbb {D}} \). Due to the choice of the weight, we can include in consideration the case when the real part of the complex power of the operator degenerates. We prove the estimates of Zygmund type for the modulus of continuity, and then we obtain the corresponding weighted boundedness result.

中文翻译：

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广义变量 Hölder 空间中变量阶分数积分算子的加权估计

本文致力于在单位圆盘\( {\mathbb {D}} \)上的全纯函数的广义变量 Hölder 空间中对 Bergman 型变量阶的分数积分算子进行加权估计。由于权重的选择，我们可以考虑算子复数幂的实部退化的情况。我们证明了Zygmund类型对连续模的估计，然后我们得到了相应的加权有界结果。