L_p-极投影Brunn-Minkowski不等式  

L_p-Polar Projection Brunn-Minkowski Inequality

作　　者：赵长健[1] 张荣森[2] 

机构地区：[1]中国计量学院数学系,杭州310018 [2]香港大学数学系

出　　处：《数学年刊（A辑）》2010年第2期239-246,共8页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.10971205);香港特别行政区研究资助局(No.HKU7016/07P)资助的项目

摘　　要：将经典的对偶混合体积概念推广到L_p空间,提出了"q-全对偶混合体积"的概念.将传统的p≥1的L_p投影体概念拓展,提出p<1时的L_p投影体和混合投影体概念,并且建立了L_p-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L_p空间的极形式.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.

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 

分 类 号：O178[理学—数学]