In this paper, we establish functional forms of the Orlicz Brunn-Minkowski inequality and the Orlicz-Minkowski inequality for the electrostatic -capacity, which generalize previous results by Zou and Xiong. We also show that these two inequalities are equivalent.

中文翻译：

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容量的函数Orlicz Brunn-Minkowski不等式

在本文中，我们建立期Orlicz布鲁恩，闵可夫斯基不等式和期Orlicz -闵可夫斯基不等式静电的功能形式-容量，推广由邹和熊之前的结果。我们还表明这两个不等式是等效的。