论文标题
加权伯瓦尔德的不平等
Weighted Berwald's Inequality
论文作者
论文摘要
伯瓦尔德的不平等是一种反向 - hölder，例如$ p $ th平均值的不平等，$ p \ in（-1，\ infty），$的$ p \ in（-1，\ infty），$的$ the $ \ mathbb {r}^n。$ \ mathbb {r}^n。$ n。$ conteve berwald的情况，我们对函数的等式进行了等值，以供您使用的情况。 $ s $ -concave度量，$ s \ in \ mathbb {r}。$我们还获得平等条件；特别是，这为伯瓦尔德经典不平等的平等条件提供了新的证据。作为应用，我们概括了许多经典的边界，以衡量凸体与半空间的交点，以及径向含义物体的概念和凸体的投射体。
The inequality of Berwald is a reverse-Hölder like inequality for the $p$th average, $p\in (-1,\infty),$ of a non-negative, concave function over a convex body in $\mathbb{R}^n.$ We prove Berwald's inequality for averages of functions with respect to measures that have some concavity conditions, e.g. $s$-concave measures, $s\in \mathbb{R}.$ We also obtain equality conditions; in particular, this provides a new proof for the equality conditions of the classical inequality of Berwald. As applications, we generalize a number of classical bounds for the measure of the intersection of a convex body with a half-space and also the concept of radial means bodies and the projection body of a convex body.
