论文标题
Sobolev空间的痕迹到不规则的度量测量空间子集
Traces of Sobolev spaces to irregular subsets of metric measure spaces
论文作者
论文摘要
给定（1，\ infty）$，让$（\ operatorName {x}，\ pereratatorName {d}，μ）$是一个度量度量空间，并在本地均匀倍增$μ$支撑弱本地$（1，p）$ - POINCARRE的平等。对于[0，p）$中的每个$θ\，我们表征了Sobolev $ W^{1} _ {p}（\ operatorAtorName {x}）$ - 降低codimension- $θ$ content-contraceimension- $θ$常规封闭的子集$ s \ subset $ subset \ perperatoRateOrname {x x} $的空间。特别是，如果空间$（\ operatorName {x}，\ operatorname {d}，μ）$ as ahlfors $ q $ - 某些$ q \ geq 1 $和$ p \ in（q，\ infty）$的geq \ geq 1 $和$ p \ in（q，\ infty）$ $ w^{1} _ {p}（\ operatorname {x}）$ - 任意封闭的非空置设置$ s \ subset \ operatatorName {x} $的空间。
Given $p \in (1,\infty)$, let $(\operatorname{X},\operatorname{d},μ)$ be a metric measure space with uniformly locally doubling measure $μ$ supporting a weak local $(1,p)$-Poincaré inequality. For each $θ\in [0,p)$, we characterize the trace space of the Sobolev $W^{1}_{p}(\operatorname{X})$-space to lower codimension-$θ$ content regular closed subsets $S \subset \operatorname{X}$. In particular, if the space $(\operatorname{X},\operatorname{d},μ)$ is Ahlfors $Q$-regular for some $Q \geq 1$ and $p \in (Q,\infty)$, then we get an intrinsic description of the trace-space of the Sobolev $W^{1}_{p}(\operatorname{X})$-space to arbitrary closed nonempty set $S \subset \operatorname{X}$.
