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- W2003233614 abstract "Abstract 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 ( G K ), 1 ≤ p < ∞, which contain ( G ) and with dim(ℳ/( z - λ )ℳ) = 1 for all λ ∈ G K . When G K is connected, we will see that dim(ℳ/( z - λ )ℳ) = 1 for all λ ∈ G K and thus in this case we will have a complete description of the invariant subspaces lying between ( G ) and ( G K ). When p = ∞, we will remark on the structure of the weak-star closed z -invariant subspaces between H ∞ ( G ) and H ∞ ( G K ). When G K is not connected, we will show that in general the invariant subspaces between ( G ) and ( G K ) are fantastically complicated. As an application of these results, we will remark on the complexity of the invariant subspaces (under ƒ → ζƒ) of certain Besov spaces on K . In particular, we shall see that in the harmonic Dirichlet space , there are invariant subspaces ℱ such that the dimension of ζℱ in ℱ is infinite." @default.
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- W2003233614 date "1996-04-01" @default.
- W2003233614 modified "2023-09-29" @default.
- W2003233614 title "Bergman Spaces on Disconnected Domains" @default.
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- W2003233614 doi "https://doi.org/10.4153/cjm-1996-011-5" @default.
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