On the H.-Q. Li inequality on step-two Carnot groups
In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q. Li inequality. As a byproduct, we provide a...
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| Format: | Article |
| Language: | English |
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Académie des sciences
2023-10-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.475/ |
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| author | Zhang, Ye |
| author_facet | Zhang, Ye |
| author_sort | Zhang, Ye |
| collection | DOAJ |
| description | In this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q. Li inequality. As a byproduct, we provide a simpler proof of the fact that the constant in H.-Q. Li inequality is strictly larger than $1$. |
| format | Article |
| id | doaj-art-e167ffd17ece444f9a6d6fb4e6183e7a |
| institution | Kabale University |
| issn | 1778-3569 |
| language | English |
| publishDate | 2023-10-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Mathématique |
| spelling | doaj-art-e167ffd17ece444f9a6d6fb4e6183e7a2025-02-07T11:09:55ZengAcadémie des sciencesComptes Rendus. Mathématique1778-35692023-10-01361G71107111410.5802/crmath.47510.5802/crmath.475On the H.-Q. Li inequality on step-two Carnot groupsZhang, Ye0Analysis on Metric Spaces Unit, Okinawa Institute of Science and Technology Graduate University, Okinawa 904-0495, JapanIn this note we show that the gradient estimate of the heat semigroup, or more precisely the H.-Q. Li inequality, is preserved under tensorization, some suitable group epimorphism, and central sum. We also establish the Riemannian counterpart of the H.-Q. Li inequality. As a byproduct, we provide a simpler proof of the fact that the constant in H.-Q. Li inequality is strictly larger than $1$.https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.475/ |
| spellingShingle | Zhang, Ye On the H.-Q. Li inequality on step-two Carnot groups Comptes Rendus. Mathématique |
| title | On the H.-Q. Li inequality on step-two Carnot groups |
| title_full | On the H.-Q. Li inequality on step-two Carnot groups |
| title_fullStr | On the H.-Q. Li inequality on step-two Carnot groups |
| title_full_unstemmed | On the H.-Q. Li inequality on step-two Carnot groups |
| title_short | On the H.-Q. Li inequality on step-two Carnot groups |
| title_sort | on the h q li inequality on step two carnot groups |
| url | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.475/ |
| work_keys_str_mv | AT zhangye onthehqliinequalityonsteptwocarnotgroups |