| 对偶L_p-质心体与Fourier变换 |
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| 引用本文： | 冷岗松,吕松军,袁俊.对偶L_p-质心体与Fourier变换[J].数学学报,2007,50(6):1419-142. |
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| 作者姓名： | 冷岗松 吕松军 袁俊 |
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| 作者单位： | 上海大学数学系，重庆师范大学数学与计算机科学学院，南京师范大学数学与计算机科学学院 上海 200444，重庆 400047，南京 210097 |
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| 基金项目： | 国家自然科学基金(10671117) |
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| 摘 要： | 对p>0,Lutwak,Yang和Zhang引进了R~n中一个凸体K的对偶L_p~-质心体Γ_(-p)K.本文研究Γ_(-p)KΓ_(-p)L是否必定蕴涵vol_n(K)≤vol_n(L)的问题.我们的结果是Lutwak(p=1的情形)及Grinberg和Zhang(p>1的情形)关于L_(p~-)质心体算子Γ_p的类似问题的结果的对偶形式.
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| 关 键 词： | 凸体 对偶p-质心体 嵌入到L_p Fourier变换 |
| 文章编号： | 0583-1431（2007）06-1419-06 |
| 收稿时间： | 2006-12-15 |
| 修稿时间： | 2006-12-25 |
Dual L_p-Centroid Bodies and the Fourier Transform |
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| Gang Song LENG,Song Jun LV,Jun YUAN.Dual L_p-Centroid Bodies and the Fourier Transform[J].Acta Mathematica Sinica,2007,50(6):1419-142. |
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| Authors: | Gang Song LENG Song Jun LV Jun YUAN |
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| Institution: | 1.Department of Mathematics, Shanghai University, Shanghai 200444, P. R. China;2. School of Mathematics and Computer Science, Chongqing Normal University, Chongqing 400047, P. R. China;3.School of Mathematics and Computer Science, Nanjing Normal University, Nanjing 210097, P. R.China |
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| Abstract: | For p>0,Lutwak,Yang and Zhang introduced a star bodyΓ_(-p)K of a convex body K.In this paper we consider the question of whetherΓ_(-p)KΓ_(-p)L implies vol_n(K)(?)vol_n(L).Our results are dual forms for the studies ofΓ_p by Lutwak in the case p=1 and by Grinberg and Zhang in the case p>1. |
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| Keywords: | convex body dual p-centroid body embedding in L_p Fourier transform |
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