| 球面上的次临界最佳Sobolev不等式 |
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| 引用本文： | 王胜军,张书陶,韩亚洲.球面上的次临界最佳Sobolev不等式[J].数学进展,2021(2):239-244. |
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| 作者姓名： | 王胜军 张书陶 韩亚洲 |
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| 作者单位： | 青海师范大学数学与统计学院;中国计量大学理学院 |
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| 基金项目： | Supported by NSFC(No.11201443);Natural Science Foundation of Zhejiang Province(No.LY18A010013)。 |
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| 摘 要： | 本文在球面SN上建立了一类最佳Sobolev不等式:||∫||2LqSN≤(q-2)Γ(N-d/2+1/dΓ(N+d/2)(∫SNf(§d§-Γ(N+d/2)/Γ(N-d)/2∫S^(N|∫|2d§),其中Ad(0N的高阶保形算子,d§SN的归一化曲面测度,2≤q<2N/N-d.
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| 关 键 词： | 最佳Sobolev不等式 最佳Hardy-Littlewood-Sobolev不等式 |
Sharp Sobolev Inequalities on the Sphere:Subcritical Case |
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| WANG Shengjun,ZHANG Shutao,HAN Yazhou.Sharp Sobolev Inequalities on the Sphere:Subcritical Case[J].Advances in Mathematics,2021(2):239-244. |
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| Authors: | WANG Shengjun ZHANG Shutao HAN Yazhou |
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| Institution: | (School of Mathematics and Statistics,Qinghai Normal University,Xining,Qinghai,810008,P.R.China;College of Science,China Jiliang University,Hangzhou,Zhejiang,310018,P.R.China) |
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| Abstract: | This paper is devoted to establishing a class of sharp Sobolev inequalities on the sphere SN,which have the form||∫||2LqSN≤(q-2)Γ(N-d/2+1/dΓ(N+d/2)(∫SNf(§d§-Γ(N+d/2)/Γ(N-d)/2∫S^(N|∫|2d§),where Ad(0Nand 2≤q<2N/N-d. |
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| Keywords: | sharp Sobolev inequality sharp Hardy-Littlewood-Sobolev inequality |
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