| 赵长健,张荣森.Lp-极投影Brunn-Minkowski不等式[J].数学年刊A辑,2010,31(2):239~246 |
| Lp-极投影Brunn-Minkowski不等式 |
| Lp-Polar Projection Brunn-Minkowski Inequality |
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| DOI： |
| 中文关键词: q-对偶混合体积 Lp-极投影体 Lp-混合投影体 Brunn-Minkowski不等式 |
| 英文关键词:q-dual mixed volumes Lp-polar projection bodies Lp-mixed pro jection bodies Brunn-Minkowski inequality |
| 基金项目:国家自然科学基金，香港特别行政区研究资助局资助项目 |
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| 中文摘要: |
| 将经典的对偶混合体积概念推广到Lp空间,提出了"q-全对偶混合体积"的概念.将传统的P≥1的Lp投影体概念拓展,提出P<1时的Lp投影体和混合投影体概念,并且建立了Lp-极投影Brunn-Minkowski不等式.作为应用,推广了熟知的极投影Brunn-Minkowski不等式,获得了投影Brunn-Minkowski不等式的Lp空间的极形式. |
| 英文摘要: |
| In this paper, the authors first generalize the notion of classical dual mixed volume to Lp-space and introduce the notion of q-dual mixed volume. Moreover, they extend the notion of classical Lp(p≥1)-projection bodies and introduce the notions of Lp(p < 1)-projection and mixed projection bodies, and establish the Brunn-Minkowski inequality for Lp-polar mixed projection bodies. As applications, the well-known Brunn-Minkowski inequality for polar of projection bodies is generalized and an Lp-polar form of Brunn-Minkowski inequality for projection bodies is obtained. |
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