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- W2015705440 abstract "Let E be a compact set in the complex plane with positive Lebesgue measure, and denote by Rp(E), p ⩾ 1, the closure in the Lp(E) norm of the rational functions with poles off E. A point z ϵ E is said to be a bounded point evaluation for Rp(E) if the map z ƒ(z), defined for the rational functions, can be extended to a bounded linear functional on Rp(E). For p < 2 there are no other bounded point evaluations for Rp(E) than the interior points of E, but for p ⩾ 2 there may be bounded point evaluations on the boundary, ∂E. We give a condition, in terms of capacity, which is necessary and sufficient for a point on ∂E to be a bounded point evaluation for Rp(E), 2 < p < ∞, and close to necessary and sufficient when p = 2. We also treat bounded point derivations, and the corresponding problems for Lp-spaces of analytic functions on open sets." @default.
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- W2015705440 date "1972-07-01" @default.
- W2015705440 modified "2023-10-03" @default.
- W2015705440 title "Bounded point evaluations and capacity" @default.
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- W2015705440 doi "https://doi.org/10.1016/0022-1236(72)90026-2" @default.
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