Sharp trace inequalities for conformally invariant fractional powers of the sublaplacian on the Heisenberg group and the CR sphere
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908975777185792 |
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| author | Yang, Qiaohua Yu, Leyuan |
| author_facet | Yang, Qiaohua Yu, Leyuan |
| contents | We establish sharp Sobolev trace inequalities for conformally invariant fractional powers of the sublaplacian on the Heisenberg group and the CR sphere, extending the corresponding Euclidean results of Einav-Loss, Beckner, and Bez-Machihara-Sugimoto to these non-Euclidean settings. In the limiting case, sharp trace Beckner-Onofri inequalities are also established on the CR sphere. The proofs are based on a duality argument due to Bez-Machihara-Sugimoto, together with the Frank-Lieb sharp form of the Hardy-Littlewood-Sobolev inequalities on the Heisenberg group and the CR sphere. The same approach also yields trace Beckner-Onofri inequalities on the standard sphere. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_16771 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Sharp trace inequalities for conformally invariant fractional powers of the sublaplacian on the Heisenberg group and the CR sphere Yang, Qiaohua Yu, Leyuan Analysis of PDEs We establish sharp Sobolev trace inequalities for conformally invariant fractional powers of the sublaplacian on the Heisenberg group and the CR sphere, extending the corresponding Euclidean results of Einav-Loss, Beckner, and Bez-Machihara-Sugimoto to these non-Euclidean settings. In the limiting case, sharp trace Beckner-Onofri inequalities are also established on the CR sphere. The proofs are based on a duality argument due to Bez-Machihara-Sugimoto, together with the Frank-Lieb sharp form of the Hardy-Littlewood-Sobolev inequalities on the Heisenberg group and the CR sphere. The same approach also yields trace Beckner-Onofri inequalities on the standard sphere. |
| title | Sharp trace inequalities for conformally invariant fractional powers of the sublaplacian on the Heisenberg group and the CR sphere |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.16771 |