Orlicz对偶混合均质积分

数学物理学报 ›› 2016, Vol. 36 ›› Issue (5): 861-872.

Orlicz对偶混合均质积分

孙宝磊^1,2, 姚纯青²

1. 重庆市杨家坪中学重庆 400050;
2. 西南大学数学与统计学院重庆 400715

收稿日期:2015-12-21 修回日期:2016-06-30 出版日期:2016-10-26 发布日期:2016-10-26
通讯作者: 姚纯青,E-mail:yaocq@swu.edu.cn E-mail:yaocq@swu.edu.cn
作者简介:孙宝磊,E-mail:xiaobao091030111@126.com;姚纯青,E-mail:yaocq@swu.edu.cn
基金资助:
国家自然科学基金（11471188）资助

Orlicz Dual Mixed Quermassintegrls

Sun Baolei^1,2, Yao Chunqing²

1. Chongqing Yangjiaping Middle School, Chongqing 400050;
2. School of Mathematics and Statistics, Southwest University, Chongqing 400715

Received:2015-12-21 Revised:2016-06-30 Online:2016-10-26 Published:2016-10-26
Supported by:
Supported by the NSFC (11471188)

摘要/Abstract

摘要：

该文讨论了Orlicz对偶混合均质积分的连续性、唯一性，给出了在一般线性变换下的性质，证明了关于Orlicz对偶混合均质积分的循环不等式，同时证明了关于Orlicz对偶混合均质积分的对偶Orlicz-Minkowski不等式与对偶均质积分关于调和Orlicz组合的对偶Orlicz-Brunn-Minkowski不等式是等价的，还得到了对偶Orlicz-Cauchy-Kubota公式.

关键词: Orlicz对偶混合均质积分, 线性变换, 对偶Orlicz-Minkowski不等式, 对偶Orlicz-Brunn-Minkowski不等式, 对偶Orlicz-Cauchy-Kubota公式

Abstract:

In this paper, we shows the continuity and the uniqueness result of the Orlicz dual mixed quermassintegrls, prove a property of the Orlicz dual mixed quermassintegrls under linear transformation. Further, the circulate inequality for the Orlicz dual mixed quermassintegrls is obtained. The equivalence between the dual Orlicz-Minkowski inequality for dual Orlicz mixed quermassintegrals and the dual Orlicz-Brunn-Minkowski inequality for Orlicz radial combination are demonstrated. We generalize the dual Orlicz-Cauchy-Kubota formula.

Key words: Orlicz dual mixed quermassintegrls, Linear transformation, Dual Orlicz-Minkowski inequality, Dual Orlicz-Brunn-Minkowski inequality, Dual Orlicz-Cauchy-Kubota formula

中图分类号:

O186.5

孙宝磊, 姚纯青. Orlicz对偶混合均质积分[J]. 数学物理学报, 2016, 36(5): 861-872.

Sun Baolei, Yao Chunqing. Orlicz Dual Mixed Quermassintegrls[J]. Acta mathematica scientia,Series A, 2016, 36(5): 861-872.

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