Solvability of the Gleason problem on a class of bounded pseudoconvex domains
Abstract
We show that if a bounded pseudoconvex domain satisfies the solvability of the bounded ∂ 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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