Matsuzaki [M1] introduced the Teichmüller space \(T_{0}^{\alpha }\) of diffeomorphisms of the unit circle with Hölder continuous derivatives and investigated its Schwarzian derivative model. This paper deals with the pre-Schwarzian derivative model \(T_{0}^{\alpha }(1)\) of the Teichmüller space \(T_{0}^{\alpha }\). It is shown that \(T_{0}^{\alpha }(1)\) is a connected open subset of \({\mathcal {B}}_{0}^{\alpha }(\Delta )\) and the pre-Bers projection is a holomorphic split submersion in \(T_{0}^{\alpha }\).

中文翻译：

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具有Hölder连续导数的圆微分形的Teichmüller空间

Matsuzaki [M1]引入了带有Hölder连续导数的单位圆微分态的Teichmüller空间\（T_ {0} ^ {\ alpha} \），并研究了其Schwarzian导数模型。本文讨论了Teichmüller空间\（T_ {0} ^ {\ alpha} \）的前Schwarzian导数模型\（T_ {0} ^ {\ alpha}（1）\）。证明\（T_ {0} ^ {\ alpha}（1）\）是\（{\ mathcal {B}} _ {0} ^ {\ alpha}（\ Delta} \）的连接开放子集而前Bers投影是\（T_ {0} ^ {\ alpha} \）中的全纯分裂淹没。