Support points for families of univalent mappings on bounded symmetric domains

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2020,（12）
• 所属期刊栏目: Articles
• 页码范围: 2379-2398
• 页数: 20页
• 语种: 英文

摘要

In this paper,we study some extremal problems for the family S0q(Bx)of normalized univalent mappings with g-parametric representation on the unit ball Bx of an n-dimensional JB*-triple X with r ≥ 2,where r is the rank of X and g is a convex(univalent)function on the unit disc U,which satisfies some natural assumptions.We obtain sharp coefficient bounds for the family S0g(Bx),and examples of bounded support points for various subsets of S0g(Bx).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 Bn and the unit polydisc Un in Cn.Certain questions will be also mentioned.Finally,we point out sharp coefficient bounds and bounded support points for the family S0g(Bn)and for special compact subsets of S0g(Bn),in the case n ≥ 2.