In this paper, we define the \(L_p\)-mixed affine surface area probability measure and obtain the log-Minkowski inequalities for nonsymmetric convex bodies of \(L_p\)-mixed affine surface area. Besides, we also establish the functional inequalities for \(L_p\)-mixed affine surface area, which are more general form than the log-Minkowski inequalities of \(L_p\)-mixed affine surface area.

中文翻译：

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$$ L_p $$ L p-混合仿射表面积的一些log-Minkowski不等式

在本文中，我们定义了\（L_p \）混合仿射表面积的概率度量，并获得了\（L_p \）混合仿射表面积的非对称凸体的log-Minkowski不等式。此外，我们还建立了泛函不等式\（L_P \） -mixed仿射表面积，这比的对数闵可夫斯基不等式更一般的形式\（L_P \） -mixed仿射表面积。