The Daugavet property for Sobolev spaces over the plane
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2026
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| Acceso en línea: | |
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| _version_ | 1866917231353397248 |
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| author | Hamad, Samir |
| author_facet | Hamad, Samir |
| contents | We show that $W^{1,1}(\mathbb{R}^2)$ has the Daugavet property when endowed with the norm induced by the $L^1$-norm of the gradient, but fails to have the slice diameter two property when equipped with the usual Sobolev norm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_21486 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The Daugavet property for Sobolev spaces over the plane Hamad, Samir Functional Analysis 46B20, 46B04, 46E35 We show that $W^{1,1}(\mathbb{R}^2)$ has the Daugavet property when endowed with the norm induced by the $L^1$-norm of the gradient, but fails to have the slice diameter two property when equipped with the usual Sobolev norm. |
| title | The Daugavet property for Sobolev spaces over the plane |
| topic | Functional Analysis 46B20, 46B04, 46E35 |
| url | https://arxiv.org/abs/2601.21486 |