Orlicz dual of log-Aleksandrov-Fenchel inequality. (English) Zbl 1524.46047
Summary: In this paper, we establish an Orlicz dual of the log-Aleksandrov-Fenchel inequality, by introducing two new concepts of dual mixed volume measures, and using the newly established Orlicz dual Aleksandrov-Fenchel inequality. The Orlicz dual log-Aleksandrov-Fenchel inequality in special cases yields the classical dual Aleksandrov-Fenchel inequality and some dual logarithmic Minkowski-type inequalities, respectively. Moreover, the dual log-Aleksandrov-Fenchel inequality is therefore also derived.
MSC:
| 46E30 | Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) |
| 52A39 | Mixed volumes and related topics in convex geometry |
Keywords:
dual mixed volume; \(L_p\)-dual mixed volume; Orlicz multiple dual mixed volume; dual logarithmic Minkowski inequality; dual Aleksandrov-Fenchel inequalityReferences:
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