对偶L_p-质心体与Fourier变换

冷岗松;吕松军;袁俊;

数学学报 ›› 2007, Vol. 50 ›› Issue (6) : 1419-142.

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中国科学院数学与系统科学研究院期刊网
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数学学报 ›› 2007, Vol. 50 ›› Issue (6) : 1419-142. DOI: 10.12386/A2007sxxb0166
论文

对偶L_p-质心体与Fourier变换

    冷岗松;吕松军;袁俊;
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Dual L_p-Centroid Bodies and the Fourier Transform

    Gang Song LENG(1); Song Jun LV
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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)KΓ_(-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.

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)KΓ_(-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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凸体 / 嵌入到L_p / Fourier变换 / 对偶p-质心体

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冷岗松;吕松军;袁俊;. 对偶L_p-质心体与Fourier变换. 数学学报, 2007, 50(6): 1419-142 https://doi.org/10.12386/A2007sxxb0166
Gang Song LENG(1); Song Jun LV. Dual L_p-Centroid Bodies and the Fourier Transform. Acta Mathematica Sinica, Chinese Series, 2007, 50(6): 1419-142 https://doi.org/10.12386/A2007sxxb0166
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