We introduce and study the variable generalized Hölder spaces of holomorphic functions over the unit disc in the complex plane. These spaces are defined either directly in terms of modulus of continuity or in terms of estimates of derivatives near the boundary. We provide conditions of Zygmund type for imbedding of the former into the latter and vice versa. We study mapping properties of variable order fractional integrals in the frameworks of such spaces.

中文翻译：

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全纯函数的可变广义 Hölder 空间中的变阶分数积分

我们介绍并研究了复平面单位圆盘上全纯函数的可变广义霍尔德空间。这些空间是直接根据连续性模数或根据边界附近导数的估计来定义的。我们提供了 Zygmund 类型的条件，用于将前者嵌入到后者中，反之亦然。我们在这种空间的框架中研究变阶分数积分的映射特性。