The Roper-Suffridge extension operator and its applications to convex mappings in C2
The Roper-Suffridge extension operator and its applications to convex mappings in C2
复制标题
Roper-Suffridge 扩展算子及其在 C2 凸映射中的应用
DOI：
10.1090/tran/7221
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发表时间：
2018
影响因子：
1.3
通讯作者：
Taishun Liu
中科院分区：
文献类型：
--
作者：
Jianfei Wang;Taishun Liu
The purpose of this paper is twofold. The first is to investigate the Roper-Suffridge extension operator which maps a biholomorhic functiononto a biholomorphic mappingon\begin {equation*}\Omega _ {n, p_ {2},\cdots, p_ {n}}(D)=\left\{(z_1, z_0)\in D\times {\mathbb {C}}^{n-1}:\sum\limits _ {j= 2}^{n}| z_ {j}|^{p_ {j}}<\frac {1}{\lambda _ {D}(z_1)}\right\}, p_j\geq 1,\end {equation*} whereandis the density of the Poincarmetric on a simply connected domain. We prove this Roper-Suffridge extension operator preserves-starlike mapping: ifis-starlike, then so is. As a consequence, we solve a problem of Graham and Kohr in a new method. By introducing the scaling method, the second part is to construct some new convex mappings of domainwith, which can be applied to discuss the extremal point of convex mappings on the domain. This scaling idea can be viewed as providing an alternative approach to studying convex mappings on. Moreover, we propose some problems. References
The purpose of this paper is twofold. The first is to investigate the Roper-Suffridge extension operator which maps a biholomorhic functiononto a biholomorphic mappingon\begin {equation*}\Omega _ {n, p_ {2},\cdots, p_ {n}}(D)=\left\{(z_1, z_0)\in D\times {\mathbb {C}}^{n-1}:\sum\limits _ {j= 2}^{n}| z_ {j}|^{p_ {j}}<\frac {1}{\lambda _ {D}(z_1)}\right\}, p_j\geq 1,\end {equation*} whereandis the density of the Poincarmetric on a simply connected domain. We prove this Roper-Suffridge extension operator preserves-starlike mapping: ifis-starlike, then so is. As a consequence, we solve a problem of Graham and Kohr in a new method. By introducing the scaling method, the second part is to construct some new convex mappings of domainwith, which can be applied to discuss the extremal point of convex mappings on the domain. This scaling idea can be viewed as providing an alternative approach to studying convex mappings on. Moreover, we propose some problems. References