数学年刊A辑
數學年刊A輯
수학년간A집
CHINESE ANNALS OF MATHEMATICS,SERIES A
2010年
2期
239-246
,共8页
q-对偶混合体积%Lp-极投影体%Lp-混合投影体%Brunn-Minkowski不等式
q-對偶混閤體積%Lp-極投影體%Lp-混閤投影體%Brunn-Minkowski不等式
q-대우혼합체적%Lp-겁투영체%Lp-혼합투영체%Brunn-Minkowski불등식
q-dual mixed volumes%Lp-polar projection bodies%Lp-mixed pro jection bodies%Brunn-Minkowski inequality
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.
將經典的對偶混閤體積概唸推廣到Lp空間,提齣瞭"q-全對偶混閤體積"的概唸.將傳統的P≥1的Lp投影體概唸拓展,提齣P<1時的Lp投影體和混閤投影體概唸,併且建立瞭Lp-極投影Brunn-Minkowski不等式.作為應用,推廣瞭熟知的極投影Brunn-Minkowski不等式,穫得瞭投影Brunn-Minkowski不等式的Lp空間的極形式.
장경전적대우혼합체적개념추엄도Lp공간,제출료"q-전대우혼합체적"적개념.장전통적P≥1적Lp투영체개념탁전,제출P<1시적Lp투영체화혼합투영체개념,병차건립료Lp-겁투영Brunn-Minkowski불등식.작위응용,추엄료숙지적겁투영Brunn-Minkowski불등식,획득료투영Brunn-Minkowski불등식적Lp공간적겁형식.
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.
