摘要
众所周知,对数Minkowski不等式和对数Aleksandrov-Fenchel不等式,最近已先后问世.继这之后,本文通过引进混合体积测度和φ-多元混合体积测度,并且利用新近建立的Orlicz-AleksandrovFenchel不等式和经典的Hadamard积分不等式,建立了一个Orlicz空间上的φ-对数AleksandrovFenchel不等式.这个Orliczφ-对数Aleksandrov-Fenchel不等式在特殊情况下,分别产生了Aleksandrov-Fenchel不等式,对数Minkowski不等式,Orlicz对数Minkowski不等式,对数Aleksandrov-Fenchel不等式和Lp-对数Aleksandrov-Fenchel不等式.
As everyone knows,the log-Minkowski inequality and log-Aleksandrov-Fenchel inequality have been published successively.In this paper,by introducing new concepts of mixed volume measure and φ-multiple mixed volume measure,the author establishes a φ-logarithmic Aleksandrov-Fenchel inequality in the Orlicz space,and by using the newly established Orlicz-Aleksandrov-Fenchel inequality and classical Hadamard's integral inequality.The Orlicz(^-logarithmic Aleksandrov-Fenchel inequality in special cases yields the Aleksandrov-Fenchel inequality,log-Minkowski inequality,Orlicz log-Minkowski inequality,log-Aleksandrov-Fenchel inequality,and L_(p) log-Aleksandrov-Fenchel inequality,respectively.
作者
赵长健
ZHAO Changjian(Department of Mathematics,China Jiliang University,Hangzhou 310018,China)
出处
《数学年刊（A辑）》
CSCD
北大核心
2023年第1期83-96,共14页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.11371334,No.10971205)的资助。
