Lipschitz property of harmonic mappings with respect to the pseudo-hyperbolic metric
Jie Huang, Antti Rasila, Jian-Feng Zhu
TL;DR
This paper proves that harmonic Bloch mappings are Lipschitz continuous with respect to the pseudo-hyperbolic metric, extending previous results and also establishing similar properties for harmonic quasiregular Bloch-type mappings.
Contribution
It establishes Lipschitz continuity of harmonic Bloch and quasiregular Bloch-type mappings with respect to the pseudo-hyperbolic metric, improving prior results.
Findings
Harmonic Bloch mappings are Lipschitz continuous in the pseudo-hyperbolic metric.
Extension of Lipschitz property to harmonic quasiregular Bloch-type mappings.
Improvement over previous theorems regarding composition operators on the Bloch space.
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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Taxonomy
TopicsAnalytic and geometric function theory · Geometric Analysis and Curvature Flows · Advanced Mathematical Modeling in Engineering