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arXiv · 2104.05976

Lipschitz property of harmonic mappings with respect to the pseudo-hyperbolic metric

Jie Huang·Antti Rasila·Jian-Feng Zhu
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Abstract

In this paper, we show that harmonic Bloch mappings are Lipschitz continuous with respect to the pseudo-hyperbolic metric. This result improves the corresponding result of Theorem 1 of [P. Ghatage, J. Yan, and D. Zheng, Composition operators with closed range on the Bloch space, Proc. Amer. Math. Soc. 129 (2000), 2039-2044]. Furthermore, we prove the similar property for harmonic quasiregular Bloch-type mappings.

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Jie Huang, Antti Rasila, Jian-Feng Zhu. 2021-04-13. Lipschitz property of harmonic mappings with respect to the pseudo-hyperbolic metric. https://arxiv.org/abs/2104.05976

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