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Lp-极投影Brunn—Minkowski不等式
  • ISSN号：1000-8314
  • 期刊名称：《数学年刊：A辑》
  • 时间：0
  • 分类：O186.5[理学—数学;理学—基础数学]
  • 作者机构：[1]中国计量学院数学系,杭州310018, [2]香港大学数学系,香港
  • 相关基金：国家自然科学基金（No.10971205）和香港特别行政区研究资助局（No.HKUT016/07P）资助的项目.
作者： 赵长健[1], 张荣森[2]
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, q-dual mixed volumes, Lp-polar projection bodies, Lp-mixed pro-jection bodies, Brunn-Minkowski inequality
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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期刊信息
  • 《数学年刊：A辑》
  • 中国科技核心期刊
  • 主管单位:国家教育部
  • 主办单位:复旦大学
  • 主编：李大潜
  • 地址：上海市长乐路746号
  • 邮编：200040
  • 邮箱：edcam@fudan.edu.cn
  • 电话：021-65642338
  • 国际标准刊号：ISSN：1000-8314
  • 国内统一刊号：ISSN：31-1328/O1
  • 邮发代号:4-298
  • 获奖情况:
  • 国内外数据库收录:
  • 俄罗斯文摘杂志,美国数学评论（网络版）,德国数学文摘,中国中国科技核心期刊,中国北大核心期刊（2004版）,中国北大核心期刊（2008版）,中国北大核心期刊（2011版）,中国北大核心期刊（2014版）,中国北大核心期刊（2000版）
  • 被引量:4264