English

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

Complex Variables 2021-04-14 v1

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.

Keywords

Cite

@article{arxiv.2104.05976,
  title  = {Lipschitz property of harmonic mappings with respect to the pseudo-hyperbolic metric},
  author = {Jie Huang and Antti Rasila and Jian-Feng Zhu},
  journal= {arXiv preprint arXiv:2104.05976},
  year   = {2021}
}

Comments

11 pages