New approach to affine Moser-Trudinger inequalities via Besov polar projection bodies
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Acceso en línea: | |
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| _version_ | 1866916243496239104 |
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| author | Dominguez, Oscar Li, Yinqin Tikhonov, Sergey Yang, Dachun Yuan, Wen |
| author_facet | Dominguez, Oscar Li, Yinqin Tikhonov, Sergey Yang, Dachun Yuan, Wen |
| contents | We extend the affine inequalities on $\mathbb{R}^n$ for Sobolev functions in $W^{s,p}$ with $1 \leq p < n/s$ obtained recently by Haddad-Ludwig [16, 17] to the remaining range $p \geq n/s$. For each value of $s$, our results are stronger than affine Moser-Trudinger and Morrey inequalities. As a byproduct, we establish the analog of the classical $L^p$ Bourgain-Brezis-Mironescu inequalities related to the Moser-Trudinger case $p=n$. Our main tool is the affine invariant provided by Besov polar projection bodies. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07329 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | New approach to affine Moser-Trudinger inequalities via Besov polar projection bodies Dominguez, Oscar Li, Yinqin Tikhonov, Sergey Yang, Dachun Yuan, Wen Metric Geometry Functional Analysis We extend the affine inequalities on $\mathbb{R}^n$ for Sobolev functions in $W^{s,p}$ with $1 \leq p < n/s$ obtained recently by Haddad-Ludwig [16, 17] to the remaining range $p \geq n/s$. For each value of $s$, our results are stronger than affine Moser-Trudinger and Morrey inequalities. As a byproduct, we establish the analog of the classical $L^p$ Bourgain-Brezis-Mironescu inequalities related to the Moser-Trudinger case $p=n$. Our main tool is the affine invariant provided by Besov polar projection bodies. |
| title | New approach to affine Moser-Trudinger inequalities via Besov polar projection bodies |
| topic | Metric Geometry Functional Analysis |
| url | https://arxiv.org/abs/2405.07329 |