The problem of evaluation of the norm of a composition operator acting between the spaces of holomorphic functions is quite difficult. In the Hardy and weighted Bergman spaces, the norm of the composition operator is unknown even for the choice of a fairly simple symbol. We compute the operator norm of the composition operator acting between the space of Cauchy transforms and Zygmund-type spaces. We also characterize bounded and compact composition operators acting between these spaces.

中文翻译：

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由柯西空间变换为齐格蒙德型空间的复合算子的范数

对作用在全纯函数空间之间的复合算子的范数求值的问题是相当困难的。在 Hardy 和加权 Bergman 空间中，即使选择了一个相当简单的符号，组合算子的范数也是未知的。我们计算作用在柯西变换空间和齐格蒙德型空间之间的复合算子的算子范数。我们还描述了在这些空间之间起作用的有界和紧凑组合算子。