标题： 可积的Teichmüller空间用于Weil-Petersson曲线上的分析 显示英文标题

标题： Integrable Teichmüller spaces for analysis on Weil-Petersson curves

摘要： 可积的Teichmüller空间$T_p$对于$p \geq 1$是由Beltrami系数的$p$-可积性定义的。 我们通过条件$\log h'$属于实数$p$-Besov 空间来刻画 $T_p$中的拟对称同胚$h$，在情况$p=1$中应用了某种修改。 这是作为建立双全纯对应关系的论据的一部分，从乘积$\Lambda$到同时统一化的$T_p$的$p$-Weil-Petersson 曲线进入$p$-Besov 空间。 特别是，这证明了$T_p$与实数$p$-Besov 空间之间的实解析等价性。 此外，Weil-Petersson 曲线上 Besov 函数的柯西变换可以通过这个全纯映射$\Lambda$的导数来表示，由此，此情形下的 Calderón 定理是直接的。 这也意味着，Cauchy 变换在$p$-Weil-Petersson 曲线上随着它们在 Bers 坐标中的嵌入而全纯地依赖。 显示英文摘要

摘要： The integrableTeichm\"uller space $T_p$ for $p \geq 1$ is defined by the $p$-integrability of Beltrami coefficients. We characterize a quasisymmetric homeomorphism $h$ in $T_p$ by the condition that $\log h'$ belongs to the real $p$-Besov space, with a certain modification applied in the case $p=1$. This is done as part of the arguments for establishing a biholomorphic correspondence $\Lambda$ from the product of $T_p$ for simultaneous uniformization of $p$-Weil-Petersson curves into the $p$-Besov space. In particular, this proves the real-analytic equivalence between $T_p$ and the real $p$-Besov space. Moreover, the Cauchy transform of Besov functions on Weil-Petersson curves can be expressed by the derivative of this holomorphic map $\Lambda$, and from this, the Calder\'on theorem in this setting is straightforward. It also follows that the Cauchy transforms on $p$-Weil-Petersson curves holomorphically depend on their embeddings as they vary in the Bers coordinates.