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

doi:10.1007/s10473-022-0514-0

Abstract

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 $$g(z)=\sum_{l=1}^{n}(z_{l}-a_{l})\ f_{l}(z) \ \ \mbox{ for all $z=(z_{1},z_{2},\cdots ,z_{n})\in \Omega$} \ ? $$ 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}$.

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

CLC Number:

32A37

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

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