Invariant subspaces of weighted Bergman spaces in infinitely many variables

This paper is concerned with polynomially generated multiplier invariant subspaces of the weighted Bergman space Aβ in infinitely many variables. We completely classify these invariant subspaces under the unitary equivalence. Our results not only cover cases of both the Hardy space H(D2 ) and the Bergman space A(D2 ) in infinitely many variables, but also apply in finite-variable setting.

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