Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions
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. Ins...
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Hindawi Limited
2013-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2013/178460 |
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doaj-2c377cb7b67146e7bc55ac56ab27fa0a2020-11-24T21:46:44ZengHindawi LimitedJournal of Function Spaces and Applications0972-68021758-49652013-01-01201310.1155/2013/178460178460Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic FunctionsEnrique Jordá0Ana María Zarco1Departamento de Matemática Aplicada, E. Politécnica Superior de Alcoy, Universidad Politécnica de Valencia, Plaza Ferrándiz y Carbonell 2, 03801 Alcoy, SpainDepartamento de Matemática Aplicada, E. Politécnica Superior de Alcoy, Universidad Politécnica de Valencia, Plaza Ferrándiz y Carbonell 2, 03801 Alcoy, SpainFor 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.http://dx.doi.org/10.1155/2013/178460 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Enrique Jordá Ana María Zarco |
| spellingShingle |
Enrique Jordá Ana María Zarco Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions Journal of Function Spaces and Applications |
| author_facet |
Enrique Jordá Ana María Zarco |
| author_sort |
Enrique Jordá |
| title |
Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions |
| title_short |
Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions |
| title_full |
Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions |
| title_fullStr |
Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions |
| title_full_unstemmed |
Isomorphisms on Weighed Banach Spaces of Harmonic and Holomorphic Functions |
| title_sort |
isomorphisms on weighed banach spaces of harmonic and holomorphic functions |
| publisher |
Hindawi Limited |
| series |
Journal of Function Spaces and Applications |
| issn |
0972-6802 1758-4965 |
| publishDate |
2013-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/2013/178460 |
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AT enriquejorda isomorphismsonweighedbanachspacesofharmonicandholomorphicfunctions AT anamariazarco isomorphismsonweighedbanachspacesofharmonicandholomorphicfunctions |
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1725900260602019840 |