论文标题
$ l^p $-poincaré不平等现象
$L^p$-Poincaré inequalities on nested fractals
论文作者
论文摘要
我们证明了一些嵌套的分形等级不变$ l^p $-poincaré不平等现象，范围为$ 1 \ le p \ le 2 $。我们的证明是基于使用加热核方法在分形上开发本地$ l^p $的开发。给出了缩放不平等不平等的应用，并在分形上进行了最大功能和最大功能的研究。在Vicsek集合的情况下进行了说明并进一步开发。
We prove on some nested fractals scale invariant $L^p$-Poincaré inequalities on metric balls in the range $1 \le p \le 2$. Our proof is based on the development of the local $L^p$-theory of Korevaar-Schoen-Sobolev spaces on fractals using heat kernel methods. Applications to scale invariant Sobolev inequalities and to the study of maximal functions and Hajłasz-Sobolev spaces on fractals are given. Results are illustrated and further developed in the case of the Vicsek set.
