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 $\bar{\partial }$ 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.

9 pages. Comments welcome. Submitted

References in corpus (1)

• On a theorem of Bishop and commutants of Toeplitz operators in ${\mathbb{C}}^n$