• Title/Summary/Keyword: Generalized complex ellipsoids

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A REMARK ON GENERALIZED COMPLEX ELLIPSOIDS WITH SPHERICAL BOUNDARY POINTS

  • Kodama, Akio
    • Journal of the Korean Mathematical Society
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    • v.37 no.2
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    • pp.285-295
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    • 2000
  • It is well-known that there is no analogue to the Riemann mapping theorem in the higher dimensional case. Therefore, it would be an interesting question to find sufficient conditionsl for domains to be biholomorphically equivalent to the unit bal. In this paper, we investigate this questionin the case where the given domains are generalized complex ellipsoids with spherical boundary points.

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BERGMAN TYPE OPERATORS ON SOME GENERALIZED CARTAN-HARTOGS DOMAINS

  • He, Le;Tang, Yanyan;Tu, Zhenhan
    • Journal of the Korean Mathematical Society
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    • v.58 no.6
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    • pp.1347-1365
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    • 2021
  • For µ = (µ1, …, µt) (µj > 0), ξ = (z1, …, zt, w) ∈ ℂn1 × … × ℂnt × ℂm, define $${\Omega}({\mu},t)=\{{\xi}{\in}\mathbb{B}_{n_1}{\times}{\cdots}{\times}\mathbb{B}_{n_t}{\times}\mathbb{C}^m:{\parallel}w{\parallel}^2 where $\mathbb{B}_{n_j}$ is the unit ball in ℂnj (1 ≤ j ≤ t), C(χ, µ) is a constant only depending on χ = (n1, …, nt) and µ = (µ1, …, µt), which is a special type of generalized Cartan-Hartogs domain. We will give some sufficient and necessary conditions for the boundedness of some type of operators on Lp(Ω(µ, t), ω) (the weighted Lp space of Ω(µ, t) with weight ω, 1 < p < ∞). This result generalizes the works from certain classes of generalized complex ellipsoids to the generalized Cartan-Hartogs domain Ω(µ, t).