Unitary equivalence of submodules of weighted Bergman spaces in infinitely many variables.

This paper is concerned with polynomially generated multiplier invariant subspaces of the weighted Bergman space $A_{\boldsymbol{\beta}}^2$ in infinitely many variables. We completely classify these invariant subspaces under the unitary equivalence of analytic Hilbert modules. Our results not only cover cases of both the Hardy module $H^{2}(\mathbb{D}_{2}^{\infty})$ and the Bergman module $A^{2}(\mathbb{D}_{2}^{\infty})$ in infinitely many variables, but also apply in finite-variable setting.