论文标题
Bohr Radius，用于某些谐波映射
Bohr radius for some classes of Harmonic mappings
论文作者
论文摘要
我们介绍了一般具有感官有意义的谐波映射的一般类别，定义为：\ begin {equination*} \ mathcal {s}^0_ {h+\ bar {g}}}}（m）：= \ {f = h+\ bar+\ bar {g}： \ sum_ {m = 2}^{\ infty}（γ_M| a_m |+δ_M| b_m |）\ leq m，\; m> 0 \}，\ end {qore*}其中$ h（z）= z+\ sum_ {m = 2}^{\ infty} a_mz^m $，$ g（z）= \ sum_ {m = 2}^{\ infty}^{\ infty} $ \ mathbb {d}：= \ {z \ in \ mathbb {c}：| z | | \ leq1 \} $和\ begin {equation*}γ_m，\;所有$ m \ geq2 $Δ_M\ geqα_2：= \ min \ {γ_2，δ_2\}> 0，\ end end {equation*}对于所有$ m \ geq2 $。我们获得增长定理，涵盖定理并得出$ \ Mathcal {s}^0_ {h+\ bar {g}}}（m）$的类Bohr半径。为了应用结果，我们获得了许多类别的谐波单价函数和某些单相功能的BOHR半径。
We introduce a general class of sense-preserving harmonic mappings defined as follows: \begin{equation*} \mathcal{S}^0_{h+\bar{g}}(M):= \{f=h+\bar{g}: \sum_{m=2}^{\infty}(γ_m|a_m|+δ_m|b_m|)\leq M, \; M>0 \}, \end{equation*} where $h(z)=z+\sum_{m=2}^{\infty}a_mz^m$, $g(z)=\sum_{m=2}^{\infty}b_m z^m$ are analytic functions in $\mathbb{D}:=\{z\in\mathbb{C}: |z|\leq1 \}$ and \begin{equation*} γ_m,\; δ_m \geq α_2:=\min \{γ_2, δ_2\}>0, \end{equation*} for all $m\geq2$. We obtain Growth Theorem, Covering Theorem and derive the Bohr radius for the class $\mathcal{S}^0_{h+\bar{g}}(M)$. As an application of our results, we obtain the Bohr radius for many classes of harmonic univalent functions and some classes of univalent functions.
