Physical Sciences and Mathematics Commons^™

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 L^p_a(G\K), 1 ≤ p < ∞, which contain L<sup>p_a(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 …