Journal of the Korean Mathematical Society (대한수학회지)

Korean Mathematical Society (대한수학회)
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BERGMAN TYPE OPERATORS ON SOME GENERALIZED CARTAN-HARTOGS DOMAINS

  • He, Le (School of Mathematics and Statistics Wuhan University) ;
  • Tang, Yanyan (School of Mathematics and Statistics Henan University) ;
  • Tu, Zhenhan (School of Mathematics and Statistics Wuhan University)
  • Received : 2020.12.23
  • Accepted : 2021.08.20
  • Published : 2021.11.01
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Abstract

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).

Keywords

Acknowledgement

This work was supported by the National Natural Science Foundation of China (No.12071354).

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