Weighted Lipschitz continuity, Schwarz-Pick's Lemma and Landau-Bloch's theorem for hyperbolic-harmonic mappings in $\mathbb{C}^{n}$

Sh. Chen; S. Ponnusamy; X. Wang

Weighted Lipschitz continuity, Schwarz-Pick's Lemma and Landau-Bloch's theorem for hyperbolic-harmonic mappings in $\mathbb{C}^{n}$

Complex Variables 2012-05-01 v1

Authors: Sh. Chen , S. Ponnusamy , X. Wang

Abstract

In this paper, we discuss some properties on hyperbolic-harmonic mappings in the unit ball of $\mathbb{C}^{n}$ . First, we investigate the relationship between the weighted Lipschitz functions and the hyperbolic-harmonic Bloch spaces. Then we establish the Schwarz-Pick type theorem for hyperbolic-harmonic mappings and apply it to prove the existence of Landau-Bloch constant for mappings in $\alpha$ -Bloch spaces.

Keywords

hyperbolic-harmonic mappings weighted lipschitz continuity schwarz-pick lemma landau-bloch theorem bloch spaces unit ball

Cite

@article{arxiv.1204.6690,
  title  = {Weighted Lipschitz continuity, Schwarz-Pick's Lemma and Landau-Bloch's theorem for hyperbolic-harmonic mappings in $\mathbb{C}^{n}$},
  author = {Sh. Chen and S. Ponnusamy and X. Wang},
  journal= {arXiv preprint arXiv:1204.6690},
  year   = {2012}
}

Comments

13 pages; The article is with a journal for publication

Weighted Lipschitz continuity, Schwarz-Pick's Lemma and Landau-Bloch's theorem for hyperbolic-harmonic mappings in $\mathbb{C}^{n}$

Abstract

Keywords

Cite

Comments

Related papers