Affine Fractional Sobolev and Isoperimetric Inequalities
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866914059308236800 |
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| author | Haddad, Julián Ludwig, Monika |
| author_facet | Haddad, Julián Ludwig, Monika |
| contents | Sharp affine fractional Sobolev inequalities for functions on $\mathbb R^n$ are established. For each $0<s<1$, the new inequalities are significantly stronger than (and directly imply) the sharp fractional Sobolev inequalities of Almgren and Lieb. In the limit as $s\to 1^-$, the new inequalities imply the sharp affine Sobolev inequality of Gaoyong Zhang. As a consequence, fractional Petty projection inequalities are obtained that are stronger than the fractional Euclidean isoperimetric inequalities and a natural conjecture for radial mean bodies is proved. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_06375 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Affine Fractional Sobolev and Isoperimetric Inequalities Haddad, Julián Ludwig, Monika Metric Geometry Functional Analysis 2020: 46E35 (Primary) 35R11, 52A40 (Secondary) Sharp affine fractional Sobolev inequalities for functions on $\mathbb R^n$ are established. For each $0<s<1$, the new inequalities are significantly stronger than (and directly imply) the sharp fractional Sobolev inequalities of Almgren and Lieb. In the limit as $s\to 1^-$, the new inequalities imply the sharp affine Sobolev inequality of Gaoyong Zhang. As a consequence, fractional Petty projection inequalities are obtained that are stronger than the fractional Euclidean isoperimetric inequalities and a natural conjecture for radial mean bodies is proved. |
| title | Affine Fractional Sobolev and Isoperimetric Inequalities |
| topic | Metric Geometry Functional Analysis 2020: 46E35 (Primary) 35R11, 52A40 (Secondary) |
| url | https://arxiv.org/abs/2207.06375 |