Hardy–Adams Inequalities on ℍ2 × ℝn-2
Let ℍ2{\mathbb{H}^{2}} be the hyperbolic space of dimension 2. Denote by Mn=ℍ2×ℝn-2{M^{n}=\mathbb{H}^{2}\times\mathbb{R}^{n-2}} the product manifold of ℍ2{\mathbb{H}^{2}} and ℝn-2(n≥3){\mathbb{R}^{n-2}(n\geq 3)}. In this paper we establish some sharp Hardy–Adams inequalities on Mn{M^{n}}, though Mn{...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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De Gruyter
2021-05-01
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| Series: | Advanced Nonlinear Studies |
| Subjects: | |
| Online Access: | https://doi.org/10.1515/ans-2021-2122 |
| _version_ | 1811280090627047424 |
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| author | Ma Xing Wang Xumin Yang Qiaohua |
| author_facet | Ma Xing Wang Xumin Yang Qiaohua |
| author_sort | Ma Xing |
| collection | DOAJ |
| description | Let ℍ2{\mathbb{H}^{2}} be the hyperbolic space of dimension 2. Denote by Mn=ℍ2×ℝn-2{M^{n}=\mathbb{H}^{2}\times\mathbb{R}^{n-2}} the product manifold of ℍ2{\mathbb{H}^{2}} and ℝn-2(n≥3){\mathbb{R}^{n-2}(n\geq 3)}. In this paper we establish some sharp Hardy–Adams inequalities on Mn{M^{n}}, though Mn{M^{n}} is not with strictly negative sectional curvature. We also show that the sharp constant in the Poincaré–Sobolev inequality on Mn{M^{n}} coincides with the best Sobolev constant, which is of independent interest. |
| first_indexed | 2024-04-13T01:08:21Z |
| format | Article |
| id | doaj.art-02eb59192fea4a0584f15d191f02c1b9 |
| institution | Directory Open Access Journal |
| issn | 1536-1365 2169-0375 |
| language | English |
| last_indexed | 2024-04-13T01:08:21Z |
| publishDate | 2021-05-01 |
| publisher | De Gruyter |
| record_format | Article |
| series | Advanced Nonlinear Studies |
| spelling | doaj.art-02eb59192fea4a0584f15d191f02c1b92022-12-22T03:09:16ZengDe GruyterAdvanced Nonlinear Studies1536-13652169-03752021-05-0121232734510.1515/ans-2021-2122Hardy–Adams Inequalities on ℍ2 × ℝn-2Ma Xing0Wang Xumin1Yang Qiaohua2School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. ChinaCollege of Science, Beijing Forestry University, Beijing100083, P. R. ChinaSchool of Mathematics and Statistics, Wuhan University, Wuhan, 430072, P. R. ChinaLet ℍ2{\mathbb{H}^{2}} be the hyperbolic space of dimension 2. Denote by Mn=ℍ2×ℝn-2{M^{n}=\mathbb{H}^{2}\times\mathbb{R}^{n-2}} the product manifold of ℍ2{\mathbb{H}^{2}} and ℝn-2(n≥3){\mathbb{R}^{n-2}(n\geq 3)}. In this paper we establish some sharp Hardy–Adams inequalities on Mn{M^{n}}, though Mn{M^{n}} is not with strictly negative sectional curvature. We also show that the sharp constant in the Poincaré–Sobolev inequality on Mn{M^{n}} coincides with the best Sobolev constant, which is of independent interest.https://doi.org/10.1515/ans-2021-2122hardy inequalitiesadams inequalitieshyperbolic spacesharp constant46e35 35j20 |
| spellingShingle | Ma Xing Wang Xumin Yang Qiaohua Hardy–Adams Inequalities on ℍ2 × ℝn-2 Advanced Nonlinear Studies hardy inequalities adams inequalities hyperbolic space sharp constant 46e35 35j20 |
| title | Hardy–Adams Inequalities on ℍ2 × ℝn-2 |
| title_full | Hardy–Adams Inequalities on ℍ2 × ℝn-2 |
| title_fullStr | Hardy–Adams Inequalities on ℍ2 × ℝn-2 |
| title_full_unstemmed | Hardy–Adams Inequalities on ℍ2 × ℝn-2 |
| title_short | Hardy–Adams Inequalities on ℍ2 × ℝn-2 |
| title_sort | hardy adams inequalities on h2 rn 2 |
| topic | hardy inequalities adams inequalities hyperbolic space sharp constant 46e35 35j20 |
| url | https://doi.org/10.1515/ans-2021-2122 |
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