Boundary Schwarz lemma for harmonic mappings having zero of order $p$

Xiao-Jin Bai, Jie Huang, Jian-Feng Zhu

Suppose $w$ is a sense-preserving harmonic mapping of the unit disk $\mathbb{D}$ such that $w(\mathbb{D})\subseteq \mathbb{D}$ and $w$ has a zero of order $p\ge 1$ at $z=0$. In this…