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The Schwarzian Derivative of a p-Valent Function

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Abstract

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.

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Funding

This work was carried out in the framework of the Russian State Assignment (grant no. 075-01095-20-00) and supported in part by the Russian Foundation for Basic Research under grant no. 20-01-00018.

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Correspondence to V. N. Dubinin.

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Russian Text © The Author(s), 2020, published in Matematicheskie Zametki, 2020, Vol. 107, No. 6, pp. 865–872.

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Dubinin, V.N. The Schwarzian Derivative of a p-Valent Function. Math Notes 107, 953–958 (2020). https://doi.org/10.1134/S0001434620050260

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  • DOI: https://doi.org/10.1134/S0001434620050260

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