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 paper, we first improve the Schwarz lemma for w, and then, we establish its boundary Schwarz lemma. Moreover, by using the automorphism of \({\mathbb D}\), we further generalize this result.

中文翻译：

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具有零阶p的调和映射的边界Schwarz引理

假设w是单位磁盘\ {{\ mathbb D} \}的保感谐波映射，使得\（w（{\ mathbb D}} \ subseteq {\ mathbb D} \）和w具有零阶\（p \ ge 1 \）在\（z = 0 \）处。在本文中，我们首先将w的Schwarz引理加以改进，然后建立其边界Schwarz引理。此外，通过使用\（{\ mathbb D} \）的自同构，我们进一步推广了这一结果。