Chord Sobolev inequalities
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866909032574353408 |
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| author | Baêta, Fernanda M. Cai, Xiaxing |
| author_facet | Baêta, Fernanda M. Cai, Xiaxing |
| contents | The paper establishes a new family of sharp analytic inequalities. Together with the fractional Sobolev inequalities of Almgren and Lieb, they form a complete class of analytic inequalities, referred to as the chord Sobolev inequalities. A close connection between these inequalities and chord isoperimetric inequalities in integral geometry is established through a functional extension of chord power integrals. The limiting cases of the chord Sobolev inequalities are derived, one of which yields a logarithmic Sobolev-type inequality. Combined with the work of Bourgain, Brezis, and Mironescu, these results complete the picture of the chord Sobolev inequalities, including their endpoint cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_15160 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Chord Sobolev inequalities Baêta, Fernanda M. Cai, Xiaxing Metric Geometry The paper establishes a new family of sharp analytic inequalities. Together with the fractional Sobolev inequalities of Almgren and Lieb, they form a complete class of analytic inequalities, referred to as the chord Sobolev inequalities. A close connection between these inequalities and chord isoperimetric inequalities in integral geometry is established through a functional extension of chord power integrals. The limiting cases of the chord Sobolev inequalities are derived, one of which yields a logarithmic Sobolev-type inequality. Combined with the work of Bourgain, Brezis, and Mironescu, these results complete the picture of the chord Sobolev inequalities, including their endpoint cases. |
| title | Chord Sobolev inequalities |
| topic | Metric Geometry |
| url | https://arxiv.org/abs/2602.15160 |