Improved Sobolev Inequalities on the Quaternionic Sphere
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866912988826435584 |
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| author | Ren, Zongxiong Yang, Zhipeng |
| author_facet | Ren, Zongxiong Yang, Zhipeng |
| contents | In this paper we establish improved Sobolev inequalities on the quaternionic sphere under higher-order moment vanishing conditions with respect to the measure \(|u|^{p^*}\,dξ\). As an application, we give a new proof of the existence of extremals for the sharp Sobolev embedding \[ S^{1,2}(S^{4n+3}) \hookrightarrow L^{2^*}(S^{4n+3}). \] |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28469 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Improved Sobolev Inequalities on the Quaternionic Sphere Ren, Zongxiong Yang, Zhipeng Analysis of PDEs Functional Analysis 35R02, 35Q41, 81Q35 In this paper we establish improved Sobolev inequalities on the quaternionic sphere under higher-order moment vanishing conditions with respect to the measure \(|u|^{p^*}\,dξ\). As an application, we give a new proof of the existence of extremals for the sharp Sobolev embedding \[ S^{1,2}(S^{4n+3}) \hookrightarrow L^{2^*}(S^{4n+3}). \] |
| title | Improved Sobolev Inequalities on the Quaternionic Sphere |
| topic | Analysis of PDEs Functional Analysis 35R02, 35Q41, 81Q35 |
| url | https://arxiv.org/abs/2603.28469 |