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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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
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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| Summary: | 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. |
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| ISSN: | 0972-6802 1758-4965 |