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- W4297201717 abstract "A set E ⊂ Ω is holomorphically dominating for Ω if $text{sup}_{zin E}|f(Z)|=text{sup}_{zin Omega}|f(z)|$ for all holomorphic functions f on Ω. As follows from a result of Stray, this property is equivalent to the inaccessibility of the Aleksandrov compactification point * (of Ω) from $Omega smallsetminus overline{E}$. Moreover, it is equivalent to a large number of other statements (old and new) of holomorphic, harmonic and topological nature, including that a certain weighted Bergman space with p = ∞ is a Banach space. We extend this to the cases of harmonic functions in ${Bbb R}^{n}$ and holomorphic functions in ${Bbb C}^{n}$. We also present some results on when weighted Bergman spaces are (quasi)-Banach spaces, the case p = ∞ being characterised by the result mentioned above." @default.
- W4297201717 created "2022-09-27" @default.
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- W4297201717 date "2002-01-01" @default.
- W4297201717 modified "2023-10-17" @default.
- W4297201717 title "Dominating Sets for Analytic and Harmonic Functions and Completeness of Weighted Bergman Spaces" @default.
- W4297201717 doi "https://doi.org/10.1353/mpr.2002.0003" @default.
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