On invariant subspaces of several variable Bergman spaces (Q583575)

The structure of the lattice of closed invariant subspaces of the analytic Toeplitz operators acting on a Bergman space is much more complicated than in the classical Hardy space setting. In the one complex variable case, the analytic invariant subspaces of Bergman spaces of planar domains have been recently investigated by \textit{S. Axler} and \textit{P. Bourdon} [Trans. Am. Math. Soc. 306, No.2, 805-817 (1988; Zbl 0658.47011). The present paper extends Axler and Bourdon's results to the several complex variable case. More precisely, the structure of the finite invariant subspaces of finite codimension of the Bergman space associated to a bounded pseudoconvex domain with a sufficiently smooth boundary in \({\mathbb{C}}^ n\) is obtained in two distinct ways.