arXiv math/96082011996-08-05math.CV

Gleason's problem in weighted Bergman space on egg domains

Guangbin Ren, Jihuai Shi

英文摘要：

In the paper, we discuss on the egg domains: $$ Ω_a=\left\{ξ=(z,w)\in\bold C^{n+m}: \ z\in\bold C^n, \ w\in\bold C^m, |z|^2+|w|^{2/a}<1\right\}, \qquad 0<a\le 2. $$ We show that Gleason's problem can be solved in the weight Bergman space on theegg domains. The proof will need the help of the recent work of the second named author on the weighted Bergman projections on this kind of domain. As an application, we obtain a multiplier theorem on the egg domains.

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