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Support points for families of univalent map**s on bounded symmetric domains

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Abstract

In this paper, we study some extremal problems for the family \(S_g^0(\mathbb{B}_X)\) of normalized univalent map**s with g-parametric representation on the unit ball \(\mathbb{B}_X\) 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 \(\mathbb{U}\), which satises some natural assumptions. We obtain sharp coecient 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 map**s on the Euclidean unit ball \(\mathbb{B}^n\) and the unit polydisc \(\mathbb{U}^n\) in ℂn. Certain questions will be also mentioned. Finally, we point out sharp coecient 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 ⩾ 2.

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Acknowledgements

The first author was supported by Japan Society for the Promotion of Science KAKENHI (Grant No. JP19K03553). The authors thank Mihai Iancu for discussions concerning Proposition 2.1.

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Authors and Affiliations

  1. Faculty of Science and Engineering, Kyushu Sangyo University, Fukuoka, 813-8503, Japan

    Hidetaka Hamada

  2. Faculty of Mathematics and Computer Science, Babeş-Bolyai University, Cluj-Napoca, 400084, Romania

    Gabriela Kohr

Authors
  1. Hidetaka Hamada
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  2. Gabriela Kohr
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Correspondence to Hidetaka Hamada.

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Dedicated to Professor Ian Graham, Our Collaborator and Friend, on the Occasion of His 70th Birthday

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Hamada, H., Kohr, G. Support points for families of univalent map**s on bounded symmetric domains. Sci. China Math. 63, 2379–2398 (2020). https://doi.org/10.1007/s11425-019-1632-1

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