Boundary Schwarz Lemma for Harmonic Mappings Having Zero of Order p

Xiao Jin Bai, Jie Huang, Jian Feng Zhu

Research output: Contribution to journalArticlepeer-review

Abstract

Suppose w is a sense-preserving harmonic mapping of the unit disk D such that w(D) ⊆ D and w has a zero of order p ≥ 1 at z = 0. In this paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of D, we further generalize this result.

MSC Codes 30C15(Primary), 31A20, 30C62(Secondary)

Keywords

  • Boundary Schwarz lemma
  • Harmonic mappings
  • Multiplicity of zeros
  • Schwarz lemma

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