Academic Journal
Remainder terms for several inequalities on some groups of Heisenberg-type
| العنوان: | Remainder terms for several inequalities on some groups of Heisenberg-type |
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| المؤلفون: | Liu HePing, Zhang An |
| المساهمون: | Zhang, A (reprint author), Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China., Peking Univ, Sch Math Sci, Beijing 100871, Peoples R China. |
| المصدر: | SCI ; CSCD ; 知网 |
| بيانات النشر: | SCIENCE CHINA-MATHEMATICS |
| سنة النشر: | 2015 |
| المجموعة: | Peking University Institutional Repository (PKU IR) / 北京大学机构知识库 |
| مصطلحات موضوعية: | remainder terms, stability, Sobolev-type inequalities, Heisenberg groups, HARDY-LITTLEWOOD-SOBOLEV, METRIC MEASURE-SPACES, SHARP CONSTANTS, MOSER-TRUDINGER, OPERATORS, SPHERE |
| الوصف: | We give estimates of the remainder terms for several conformally-invariant Sobolev-type inequalities on the Heisenberg group. By considering the variations of associated functionals, we give a stability for two dual inequalities: The fractional Sobolev (FS) and Hardy-Littlewood-Sobolev (HLS) inequalities, in terms of distance to the submanifold of extremizers. Then we compare their remainder terms to improve the inequalities in another way. We also compare, in the limit case, the remainder terms of Beckner-Onofri (BO) inequality and its dual logarithmic Hardy-Littlewood-Sobolev (Log-HLS) inequality. Besides, we also list without proof some results for other groups of Iwasawa-type. Our results generalize earlier works on Euclidean spaces of Chen et al. (2013) and Dolbeault and Jankowiak (2014) onto some groups of Heisenberg-type. We worked for "almost" all fractions especially for comparing results, and the stability of HLS is also absolutely new, even for Euclidean case. ; National Natural Science Foundation of China [11371036]; Specialized Research Fund for the Doctoral Program of Higher Education of China [2012000110059]; China Scholarship Council [201306010009] ; SCI(E) ; 中国科学引文数据库(CSCD) ; ARTICLE ; hpliu@pku.edu.cn; anzhang@pku.edu.cn ; 12 ; 2565-2580 ; 58 |
| نوع الوثيقة: | journal/newspaper |
| اللغة: | English |
| تدمد: | 1674-7283 1869-1862 |
| Relation: | SCIENCE CHINA-MATHEMATICS.2015,58,(12),2565-2580.; 1400089; http://hdl.handle.net/20.500.11897/439202; WOS:000365692100009 |
| DOI: | 10.1007/s11425-015-5070-9 |
| الاتاحة: | https://hdl.handle.net/20.500.11897/439202 https://doi.org/10.1007/s11425-015-5070-9 |
| رقم الانضمام: | edsbas.3B53C0F3 |
| قاعدة البيانات: | BASE |
| تدمد: | 16747283 18691862 |
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| DOI: | 10.1007/s11425-015-5070-9 |