关于对偶Orlicz混合均质积分的若干不等式
发布时间：2018-10-12 14:33
【摘要】：本文主要研究了对偶的Orlicz混合均质积分.对任意单调连续函数φ,我们引进了对偶的Orlicz径向和和对偶的Orlicz混合均质积分,由此建立起关于对偶的Orlicz混合均质积分的对偶的Orlicz-Minkowski不等式和对偶的Orlicz-Brunn-Minkowski不等式.这些不等式类似于Lp里特殊的情形(包括-∞p0,p = 0,0p1,p=1,和1p+∞).当φ = logt时,这些不等式和公开问题紧密相关,包括log-Minkowski问题和log-Brunn-Minkowski问题.最后,我们还证明了对偶的Orlicz-Minkowski不等式和对偶的Orlicz-Brunn-Minkowski不等式之间的等价性.
[Abstract]:In this paper, we study dual Orlicz mixed homogeneous integrals. For any monotone continuous function 蠁, we introduce dual Orlicz radial and dual Orlicz mixed homogeneous integrals, and establish dual Orlicz-Minkowski inequalities and dual Orlicz-Brunn-Minkowski inequalities for dual Orlicz mixed homogeneous integrals. These inequalities are similar to the special cases in Lp (including-鈭，
本文编号：2266485
[Abstract]:In this paper, we study dual Orlicz mixed homogeneous integrals. For any monotone continuous function 蠁, we introduce dual Orlicz radial and dual Orlicz mixed homogeneous integrals, and establish dual Orlicz-Minkowski inequalities and dual Orlicz-Brunn-Minkowski inequalities for dual Orlicz mixed homogeneous integrals. These inequalities are similar to the special cases in Lp (including-鈭，
本文编号：2266485
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