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http://dx.doi.org/10.4134/JKMS.j200689

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)
Publication Information
Journal of the Korean Mathematical Society / v.58, no.6, 2021 , pp. 1347-1365 More about this Journal
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 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
Bergman type operator; generalized Cartan-Hartogs domain; weighted Bergman space;
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