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arXiv · 2204.01121

Solvability of the Gleason problem on a class of bounded pseudoconvex domains

Timothy G. Clos
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Abstract

We show that if a bounded pseudoconvex domain satisfies the solvability of the bounded $\bar{\partial}$ problem, then the ideal of bounded holomorphic functions vanishing at a point in the domain is finitely generated. We also prove a smooth analog of the main result for bounded pseudoconvex domains with a sufficiently smooth boundary and also consider the Bergman space case.

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Timothy G. Clos. 2022-04-03. Solvability of the Gleason problem on a class of bounded pseudoconvex domains. https://doi.org/10.1007/s11785-022-01236-5

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