Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions
| Autor: | Enrique Jordá, Ana María Zarco |
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| Jazyk: | angličtina |
| Rok vydání: | 2013 |
| Předmět: | |
| Zdroj: | Journal of Function Spaces and Applications, Vol 2013 (2013) |
| Druh dokumentu: | article |
| ISSN: | 0972-6802 1758-4965 |
| DOI: | 10.1155/2013/178460 |
| Popis: | For an arbitrary open subset U⊂ℝd or U⊆ℂd and a continuous function v:U→]0,∞[ we show that the space hv0(U) of weighed harmonic functions is almost isometric to a (closed) subspace of c0, thus extending a theorem due to Bonet and Wolf for spaces of holomorphic functions Hv0(U) on open sets U⊂ℂd. Inspired by recent work of Boyd and Rueda, we characterize in terms of the extremal points of the dual of hv0(U) when hv0(U) is isometric to a subspace of c0. Some geometric conditions on an open set U⊆ℂd and convexity conditions on a weight v on U are given to ensure that neither Hv0(U) nor hv0(U) are rotund. |
| Databáze: | Directory of Open Access Journals |
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