GLEASON’S PROBLEM ON THE SPACE Fp,q,s (B) IN $\mathbb{C}^n$

GLEASON’S PROBLEM ON THE SPACE F^p,q,s (B) IN $\mathbb{C}^n$

GLEASON’S PROBLEM ON THE SPACE F^p,q,s (B) IN $\mathbb{C}^n$

GLEASON’S PROBLEM ON THE SPACE F^p,q,s (B) IN $\mathbb{C}^n$

GLEASON’S PROBLEM ON THE SPACE F^p,q,s (B) IN $\mathbb{C}^n$

GLEASON’S PROBLEM ON THE SPACE Fp,q,s (B) IN Cn\mathbb{C}^n

GLEASON’S PROBLEM ON THE SPACE Fp,q,s (B) IN Cn\mathbb{C}^n

GLEASON’S PROBLEM ON THE SPACE F^p,q,s (B) IN $\mathbb{C}^n$

GLEASON’S PROBLEM ON THE SPACE F^p,q,s (B) IN $\mathbb{C}^n$

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doi:10.1007/s10473-022-0514-0

数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (5): 1971-1980.doi: 10.1007/s10473-022-0514-0

• 论文 • 上一篇

Pengcheng TANG, Xuejun ZHANG

College of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China

收稿日期:2020-11-13 修回日期:2022-05-30 发布日期:2022-11-02
通讯作者: Xuejun Zhang,E-mail:xuejunttt@263.net E-mail:xuejunttt@263.net
基金资助:
The research was supported by the National Natural Science Foundation of China (11942109) and the Natural Science Foundation of Hunan Province (2022JJ30369).

Pengcheng TANG, Xuejun ZHANG

College of Mathematics and Statistics, Hunan Normal University, Changsha, 410081, China

Received:2020-11-13 Revised:2022-05-30 Published:2022-11-02
Contact: Xuejun Zhang,E-mail:xuejunttt@263.net E-mail:xuejunttt@263.net
Supported by:
The research was supported by the National Natural Science Foundation of China (11942109) and the Natural Science Foundation of Hunan Province (2022JJ30369).

摘要： Let $\Omega$ be a domain in $\mathbb{C}^{n}$ and let $Y$ be a function space on $\Omega$ . If $a\in \Omega$ and $g\in Y$ with $g(a)=0$ , do there exist functions $f_{1},f_{2},\cdots ,f_{n}\in Y$ such that

$g(z)=\sum_{l=1}^{n}(z_{l}-a_{l})\ f_{l}(z) \ \ \mbox{ for all $z=(z_{1},z_{2},\cdots ,z_{n})\in \Omega$} \ ?$ This is Gleason's problem. In this paper, we prove that Gleason's problem is solvable on the boundary general function space

$F^{p,q,s}(B)$ in the unit ball

$B$ of

$\mathbb{C}^{n}$ .

关键词: boundary general function space, Gleason’s problem, solvability, unit ball

Abstract: Let $\Omega$ be a domain in $\mathbb{C}^{n}$ and let $Y$ be a function space on $\Omega$ . If $a\in \Omega$ and $g\in Y$ with $g(a)=0$ , do there exist functions $f_{1},f_{2},\cdots ,f_{n}\in Y$ such that

$F^{p,q,s}(B)$ in the unit ball

$B$ of

$\mathbb{C}^{n}$ .

Key words: boundary general function space, Gleason’s problem, solvability, unit ball

中图分类号:

32A37

Pengcheng TANG, Xuejun ZHANG. GLEASON’S PROBLEM ON THE SPACE F^p,q,s (B) IN $\mathbb{C}^n$ [J]. 数学物理学报(英文版), 2022, 42(5): 1971-1980.

Pengcheng TANG, Xuejun ZHANG. GLEASON’S PROBLEM ON THE SPACE F^p,q,s (B) IN $\mathbb{C}^n$ [J]. Acta mathematica scientia,Series B, 2022, 42(5): 1971-1980.

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