Based on the quasiconformal theory of the universal Teichmüller space, we introduce the Teichmüller space of diffeomorphisms of the unit circle with $\alpha$-Hölder continuous derivatives as a subspace of the universal Teichmüller space. We characterize such a diffeomorphism quantitatively in terms of the complex dilatation of its quasiconformal extension and the Schwarzian derivative given by the Bers embedding. Then, we provide a complex Banach manifold structure for it and prove that its topology coincides with the one induced by local $C^{1+\alpha}$-topology at the base point.

中文翻译：

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具有Hölder连续导数的圆微分的Teichmüller空间

基于通用Teichmüller空间的拟保形理论，我们介绍了具有$ \ alpha $-Hölder连续导数的单位圆微分的Teichmüller空间作为通用Teichmüller空间的子空间。我们通过其准保形扩展和Bers嵌入给出的Schwarzian导数的复数膨胀来定量描述这种微晶同构。然后，我们为其提供了一个复杂的Banach流形结构，并证明其拓扑与基点上局部$ C ^ {1+ \ alpha} $-拓扑诱导的拓扑重合。