| 赵长健.Orlicz ϕ-对数Aleksandrov-Fenchel不等式*[J].数学年刊A辑,2023,44(1):83~96 |
| Orlicz ϕ-对数Aleksandrov-Fenchel不等式* |
| Orlicz ϕ-Logarithmic Aleksandrov-Fenchel Inequality |
| Received:November 16, 2020 Revised:November 02, 2022 |
| DOI：10.16205/j.cnki.cama.2023.0007 |
| 中文关键词: 混合体积, Orlicz混合体积, Orlicz-多元混合体积, 对数Minkowski不等式, Orlicz-Aleksandrov-Fenchel不等式, Hadamard积分不等式 |
| 英文关键词:Lp-Mixed volume, Orlicz mixed volume, Logarithmic Minkowski inequality, Orlicz-Aleksandrov-Fenchel inequality, Hadamard’s integral inequality |
| 基金项目:国家自然科学基金(No.11371334, No.10971205) |
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| 中文摘要: |
| 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 ?- 多元混合体积测度,并且利用新近建立的Orlicz-Aleksandrov-Fenchel不等式和经典的Hadamard积分不等式,建立了一个Orlicz空间上的 ?- 对数Aleksandrov-Fenchel不等式.这个Orlicz ?- 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. |
| 英文摘要: |
| 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 ?-multiple mixed volume measure, the author establishes a ?-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 Lp- Aleksandrov-Fenchel inequality, respectively. |
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