| Lp-极投影Brunn-Minkowski不等式 |
| |
| 引用本文： | 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). |
| |
| 作者姓名： | 赵长健 张荣森 |
| |
| 作者单位： | 1. 中国计量学院数学系,杭州,310018
2. 香港大学数学系,香港 |
| |
| 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 |
| |
| 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.
|
| 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 |
Lp-Polar Projection Brunn-Minkowski Inequality |
| |
| ZHAO Changjian,CHEUNG Wing-Sum.Lp-Polar Projection Brunn-Minkowski Inequality[J].Chinese Annals of Mathematics,Series A,2010,31(2). |
| |
| Authors: | ZHAO Changjian CHEUNG Wing-Sum |
| |
| Abstract: | 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. |
| |
| Keywords: | q-dual mixed volumes Lp-polar projection bodies Lp-mixed pro jection bodies Brunn-Minkowski inequality |
| 本文献已被 万方数据 等数据库收录！ |
