Affine Hardy--Littlewood--Sobolev inequalities
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866914057584377856 |
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| author | Haddad, Julián Ludwig, Monika |
| author_facet | Haddad, Julián Ludwig, Monika |
| contents | Sharp affine Hardy--Littlewood--Sobolev inequalities for functions on $\mathbb R^n$ are established, which are significantly stronger than (and directly imply) the sharp Hardy--Littlewood--Sobolev inequalities by Lieb and by Beckner, Dou, and Zhu. In addition, sharp reverse inequalities for the new inequalities and the affine fractional $L^2$ Sobolev inequalities are obtained for log-concave functions on $\mathbb R^n$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_12194 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Affine Hardy--Littlewood--Sobolev inequalities Haddad, Julián Ludwig, Monika Metric Geometry Functional Analysis 26D15, 26B25, 26D10, 46E35, 52A40 Sharp affine Hardy--Littlewood--Sobolev inequalities for functions on $\mathbb R^n$ are established, which are significantly stronger than (and directly imply) the sharp Hardy--Littlewood--Sobolev inequalities by Lieb and by Beckner, Dou, and Zhu. In addition, sharp reverse inequalities for the new inequalities and the affine fractional $L^2$ Sobolev inequalities are obtained for log-concave functions on $\mathbb R^n$. |
| title | Affine Hardy--Littlewood--Sobolev inequalities |
| topic | Metric Geometry Functional Analysis 26D15, 26B25, 26D10, 46E35, 52A40 |
| url | https://arxiv.org/abs/2212.12194 |