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논문 기본 정보
- 자료유형
- 학술저널
- 저자정보
- 저널정보
- 대한수학회 대한수학회지 대한수학회지 제58권 제6호
- 발행연도
- 2021.11
- 수록면
- 1,347 - 1,365 (19page)
- DOI
- 10.4134/JKMS.j200689
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초록· 키워드
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For $\mu=(\mu_1,\dots,\mu_t)$ ($\mu_j>0$), $\xi=(z_1,\dots,z_t,w)\in \mathbb{C}^{n_1}\times\cdots\times \mathbb{C}^{n_t}\times \mathbb{C}^m$, define $$\Omega(\mu,t)\!=\!\big\{\xi\in\mathbb{B}_{n_1}\times\cdots\times\mathbb{B}_{n_t}\times\mathbb{C}^{m}: \|w\|^2<C(\chi,\mu)\prod\nolimits_{j=1}^{t}(1-\|z_j\|^2)^{\mu_j}\big\},$$ where $\mathbb{B}_{n_j}$ is the unit ball in $\mathbb{C}^{n_j}$ $(1\le j\le t)$, $C(\chi,\mu)$ is a constant only depending on $\chi=(n_1,\dots,n_t)$ and $\mu=(\mu_1,\dots,\mu_t)$, 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 $L^p(\Omega(\mu,t), \omega)$ (the weighted $L^p$ space of $\Omega(\mu,t)$ with weight $\omega$, $1<p<\infty$). This result generalizes the works from certain classes of generalized complex ellipsoids to the generalized Cartan-Hartogs domain $\Omega(\mu,t)$.
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참고문헌 (26)
참고문헌 신청
Heungju Ahn / 2012 / The explicit forms and zeros of the Bergman kernel function for Hartogs type domains / Journal of Functional Analysis 262(8):3518~3547
Enchao Bi / 2016 / Balanced metrics on the Fock–Bargmann–Hartogs domains / Annals of Global Analysis and Geometry 49(4):349~359
Enchao Bi / 2018 / Rigidity of proper holomorphic mappings between generalized Fock–Bargmann–Hartogs domains / Pacific Journal of Mathematics 297(2):277~297
P. Charpentier / 2013 / Estimates for weighted Bergman projections on pseudo-convex domains of finite type in ℂ n / Complex Variables and Elliptic Equations 59(8):1070~1095
John P. D’Angelo / 1994 / An explicit computation of the Bergman kernel function / Journal of Geometric Analysis 4(1):23~34
Enchao Bi / 2016 / Balanced metrics on the Fock–Bargmann–Hartogs domains / Annals of Global Analysis and Geometry 49(4):349~359
Enchao Bi / 2018 / Rigidity of proper holomorphic mappings between generalized Fock–Bargmann–Hartogs domains / Pacific Journal of Mathematics 297(2):277~297
P. Charpentier / 2013 / Estimates for weighted Bergman projections on pseudo-convex domains of finite type in ℂ n / Complex Variables and Elliptic Equations 59(8):1070~1095
John P. D’Angelo / 1994 / An explicit computation of the Bergman kernel function / Journal of Geometric Analysis 4(1):23~34
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