论文标题
在有限的对称域上的单价映射家庭的支持点
Support points for families of univalent mappings on bounded symmetric domains
论文作者
论文摘要
在本文中，我们研究了家庭的一些极端问题$ s_g^0（\ mathbb {b} _x _x）$的标准化的单价映射，并在单位球上$ g $ -parametric表示$ \ mathbb {b} _x _x _x $ n $ n $ n $ dimensional jb $ jb $^$ - triple $ x $ $ x $ $ x $ $ $ g $是单位光盘$ \ mathbb {u} $上的凸（单价）函数，它满足了一些自然假设。我们获得了家庭的尖锐系数范围$ s_g^0（\ mathbb {b} _x）$，以及$ s_g^0的各种子集的有界支持点的示例（\ mathbb {b} _x _x）$。我们的结果是对有限的对称域的概括，这些域的最新结果与欧几里得单位球上的单价映射家族的支持点有关某些问题也将提及。最后，我们指出了家庭$ s_g^0（\ mathbb {b}^n）$的尖锐系数范围和有界的支持点，对于$ s_g^0的特殊紧凑型子集（\ Mathbb {b}^n）$，在情况下为$ n \ geq 2 $。
In this paper we study some extremal problems for the family $S_g^0(\mathbb{B}_X)$ of normalized univalent mappings with $g$-parametric representation on the unit ball $\mathbb{B}_X$ of an $n$-dimensional JB$^*$-triple $X$ with $r\geq 2$, where $r$ is the rank of $X$ and $g$ is a convex (univalent) function on the unit disc $\mathbb{U}$, which satisfies some natural assumptions. We obtain sharp coefficient bounds for the family $S_g^0(\mathbb{B}_X)$, and examples of bounded support points for various subsets of $S_g^0(\mathbb{B}_X)$. Our results are generalizations to bounded symmetric domains of known recent results related to support points for families of univalent mappings on the Euclidean unit ball $\mathbb{B}^n$ and the unit polydisc $\mathbb{U}^n$ in $\mathbb{C}^n$. Certain questions will be also mentioned. Finally, we point out sharp coefficient bounds and bounded support points for the family $S_g^0(\mathbb{B}^n)$ and for special compact subsets of $S_g^0(\mathbb{B}^n)$, in the case $n\geq 2$.
