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The Schwarzian Derivative of a p -Valent Function
Mathematical Notes ( IF 0.6 ) Pub Date : 2020-06-24 , DOI: 10.1134/s0001434620050260
V. N. Dubinin

We show that a comparison of the capacities of suitable condensers gives an inequality for the Schwarzian derivatives of a holomorphic p-valent function defined on the unit disk and ranging in a given domain of the complex plane. If that domain is a disk as well and the function is univalent, then this inequality essentially coincides with the classical Nehari inequality. The cases of equality in the resulting relation are discussed.



中文翻译:

价函数的Schwarzian导数

我们表明,对合适电容器的容量的比较给出了不等式,该不等式是在单位圆盘上定义并在复杂平面的给定范围内确定的全纯p价函数的Schwarzian导数。如果该域也是一个磁盘并且函数是单价的,则该不等式与经典的Nehari不等式实质上是一致的。讨论了所得关系中相等的情况。

更新日期:2020-06-25
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