论文标题
关于Choquet积分和Poincaré-Sobolev的不平等现象
On Choquet integrals and Poincaré-Sobolev inequalities
论文作者
论文摘要
我们认为相对于Hausdorff内容$ \ MATHCAL {H} _ \ infty^δ$，我们考虑了整体不平等。 In particular, if $Ω$ is a bounded John domain in $\mathbb{R}^n$, $n\geq 2$, and $0 <δ\le n$, we prove that the corresponding $(δp/(δ-p),p)$-Poincaré-Sobolev inequalities hold for all continuously differentiable functions defined on $Ω$ whenever $δ/n < p < δ$.我们还证明$（p，p）$ - 庞加莱的不平等对于所有$ p>Δ/n $都是有效的。
We consider integral inequalities in the sense of Choquet with respect to the Hausdorff content $\mathcal{H}_\infty^δ$. In particular, if $Ω$ is a bounded John domain in $\mathbb{R}^n$, $n\geq 2$, and $0 <δ\le n$, we prove that the corresponding $(δp/(δ-p),p)$-Poincaré-Sobolev inequalities hold for all continuously differentiable functions defined on $Ω$ whenever $δ/n < p < δ$. We prove also that the $(p,p)$-Poincaré inequality is valid for all $p>δ/n$.
