The operators and are defined by and where is an analytic self-map of the unit disc and is analytic in the disc. A characterization is provided for boundedness and compactness of the products of composition and differentiation from the spaces of fractional Cauchy transforms to the Bloch-type spaces , where and . In the case , the operator is compact is bounded and . For , is compact is bounded and .

中文翻译：

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分数柯西空间与布洛赫型空间之间的组合与微分的乘积

运算符和由定义 和 其中是单位圆盘的分析性自映射，在圆盘中进行分析。甲表征提供了用于组合物和分化从分数柯西变换的空间中的产品的有界和紧凑的布洛赫型空间，在那里 和 。在这种情况下，运算符 紧凑 有界 和 。为了， 紧凑 有界 和 。