In this paper, we first determine Bohr’s inequality for the class of harmonic mappings \(f=h+\overline{g}\) in the unit disk \(\mathbb {D}\), where either both \(h(z)=\sum _{n=0}^{\infty }a_{pn+m}z^{pn+m}\) and \(g(z)=\sum _{n=0}^{\infty }b_{pn+m}z^{pn+m}\) are analytic and bounded in \(\mathbb {D}\), or satisfies the condition \(|g'(z)|\le d|h'(z)|\) in \(\mathbb {D}\backslash \{0\}\) for some \(d\in [0,1]\) and h is bounded. In particular, we obtain Bohr’s inequality for the class of harmonic p-symmetric mappings. Also, we investigate the Bohr-type inequalities of harmonic mappings with a multiple zero at the origin and that most of results are proved to be sharp.

在本文中，我们首先确定单位磁盘\（\ mathbb {D} \）中的谐波映射\（f = h + \ overline {g} \）的玻尔不等式，其中两个\（h（z） = \ sum _ {n = 0} ^ {\ infty} a_ {pn + m} z ^ {pn + m} \）和\（g（z）= \ sum _ {n = 0} ^ {\ infty} b_ {pn + m} z ^ {pn + m} \）被解析并以\（\ mathbb {D} \）为界，或满足条件\（| g'（z）| \ le d | h'（\（\ mathbb {D} \反斜杠\ {0 \} \）中的\\ d {in [0,1] \ }中的z）| \），并且h是有界的。特别是，我们获得了谐波p类的玻尔不等式对称映射。此外，我们研究了原点具有多个零的谐波映射的Bohr型不等式，并且大多数结果都被证明是锋利的。