Loomis-Whitney inequalities on corank $1$ Carnot groups
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866911941550669824 |
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| author | Zhang, Ye |
| author_facet | Zhang, Ye |
| contents | In this paper we provide another way to deduce the Loomis-Whitney inequality on higher dimensional Heisenberg groups $\mathbb{H}^n$ based on the one on the first Heisenberg group $\mathbb{H}^1$ and the known nonlinear Loomis-Whitney inequality (which has more projections than ours). Moreover, we generalize the result to the case of corank $1$ Carnot groups and products of such groups. Our main tool is the modified equivalence between the Brascamp--Lieb inequality and the subadditivity of the entropy developed in arXiv:0710.0870v2. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_02749 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Loomis-Whitney inequalities on corank $1$ Carnot groups Zhang, Ye Classical Analysis and ODEs 26D15, 28A75, 28D20, 39B62, 43A80 In this paper we provide another way to deduce the Loomis-Whitney inequality on higher dimensional Heisenberg groups $\mathbb{H}^n$ based on the one on the first Heisenberg group $\mathbb{H}^1$ and the known nonlinear Loomis-Whitney inequality (which has more projections than ours). Moreover, we generalize the result to the case of corank $1$ Carnot groups and products of such groups. Our main tool is the modified equivalence between the Brascamp--Lieb inequality and the subadditivity of the entropy developed in arXiv:0710.0870v2. |
| title | Loomis-Whitney inequalities on corank $1$ Carnot groups |
| topic | Classical Analysis and ODEs 26D15, 28A75, 28D20, 39B62, 43A80 |
| url | https://arxiv.org/abs/2402.02749 |