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Bergman Spaces On An Annulus And The Backward Bergman Shift, William T. Ross
Bergman Spaces On An Annulus And The Backward Bergman Shift, William T. Ross
Department of Math & Statistics Technical Report Series
In this paper, we will give a complete characterization of the invariant subspaces M (under ƒ → zƒ) of the Bergman space Lpa(G), 1 < p < 2, G an annulus, which contain the constant function 1. As an application of this result, we will characterize the invariant subspaces of the adjoint of multiplication by z on the Dirichlet spaces Dq, q > 2, as well as the invariant subspaces of the backward Bergman shift ƒ → (ƒ – ƒ(0))/z on Lpa(𝔻), 1 < p < 2.
Bergman Spaces On Disconnected Domains, Alexandru Aleman, Stefan Richter, William T. Ross
Bergman Spaces On Disconnected Domains, Alexandru Aleman, Stefan Richter, William T. Ross
Department of Math & Statistics Technical Report Series
For a bounded region G ⊂ ℂ and a compact set K ⊂G , with area measure zero, we will characterize the invariant subspaces M (under ƒ → z ƒ) of the Bergman space Lpa(G\K), 1 ≤ p < ∞, which contain L<sup>pa(G) and with dim(M/(z-⋋)M) = 1 for all ⋋ ∈ G\K. When G\K is connected, we will see that dim(M/(z-⋋)M) = 1 for all ⋋ ∈ G\K and this in this case we will have a complete …