The reverse Holder inequality for an elementary function

Q3 Mathematics

Matematychni Studii Pub Date : 2021-10-23 DOI:10.30970/ms.56.1.28-38

A.O. Korenovskii

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Abstract

For a positive function $f$ on the interval $[0,1]$, the power mean of order $p\in\mathbb R$ is defined by \smallskip\centerline{$\displaystyle\|\, f\,\|_p=\left(\int_0^1 f^p(x)\,dx\right)^{1/p}\quad(p\ne0),\qquad\|\, f\,\|_0=\exp\left(\int_0^1\ln f(x)\,dx\right).$} Assume that $0

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初等函数的逆Holder不等式

对于正函数 $f$ 在间隔上 $[0,1]$，权力意味着秩序 $p\in\mathbb R$ 定义为 \smallskip\centerline{$\displaystyle\|\, f\,\|_p=\left(\int_0^1 f^p(x)\,dx\right)^{1/p}\quad(p\ne0),\qquad\|\, f\,\|_0=\exp\left(\int_0^1\ln f(x)\,dx\right).$} 假设 $0

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