Finite-codimensional invariant subspaces of Bergman spaces

Axler, Sheldon; Bourdon, Paul

doi:10.1090/S0002-9947-1988-0933319-5

Finite-codimensional invariant subspaces of Bergman spaces
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by Sheldon Axler and Paul Bourdon

Trans. Amer. Math. Soc. 306 (1988), 805-817

DOI: https://doi.org/10.1090/S0002-9947-1988-0933319-5

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Abstract:

For a large class of bounded domains in $\mathbb {C}$, we describe those finite codimensional subspaces of the Bergman space that are invariant under multiplication by $z$. Using different techniques for certain domains in ${\mathbb {C}^N}$, we describe those finite codimensional subspaces of the Bergman space that are invariant under multiplication by all the coordinate functions.

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