Support points for families of univalent mappings on bounded symmetric domains  

作　　者：Hidetaka Hamada Gabriela Kohr 

机构地区：[1]Faculty of Science and Engineering,Kyushu Sangyo University,Fukuoka 813-8503,Japan [2]Faculty of Mathematics and Computer Science,Babecs-Bolyai University,Cluj-Napoca 400084,Romania

出　　处：《Science China Mathematics》2020年第12期2379-2398,共20页中国科学：数学（英文版）

基　　金：supported by Japan Society for the Promotion of Science KAKENHI(Grant No.JP19K03553)。

摘　　要：In this paper,we study some extremal problems for the family Sg^0(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 Sg^0(BX),and examples of bounded support points for various subsets of Sg^0(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 B^n and the unit polydisc U^n in C^n.Certain questions will be also mentioned.Finally,we point out sharp coefficient bounds and bounded support points for the family Sg^0(B^n)and for special compact subsets of Sg^0(B^n),in the case n≥2.

关 键 词：bounded symmetric domain Carathéodory family g-Loewner chain parametric representation starlike mapping support point 

分 类 号：O174.5[理学—数学]