论文标题
均匀的索波列夫和besov空间的痕量和延伸定理，用于公制度量空间中无限均匀域
Trace and extension theorems for homogeneous Sobolev and Besov spaces for unbounded uniform domains in metric measure spaces
论文作者
论文摘要
在本文中，我们修复了$ 1 \ le p <\ infty $，并考虑$（\ om，d，μ）$是无限制的，本地紧凑的，不完整的度量度量空间，配备了双倍量$μ$ $ $ $ $ $ $ p $ p $-poincaré的不平等，因此$ \ om $ $ $ $ $ $ $ $ $ $ $ $ $ \ om $ \ om $ \ om $ \ om $ \ om $ \ om $ \ om \ om $ \ om $ \ om $ \ om $ \ om $ \。我们在dirichlet-sobolev space中意识到函数的痕迹$ d^{1，p}（\ om）$在边界$ \ partial \ om $上作为均质besov besov besov space $ hb^α__{p，p，p}（\ partial \ om）$的函数。在这里，$ \ partial \ om $配备了一个非原子鲍尔常规度量$ν$。我们表明，如果$ν$满足$ 0 <θ<p $ $μ$的$θ$编码状况，那么有一个有界的线性跟踪操作员$ t：d^{1，p}（\ om） $ e：hb^{1-θ/p}（\ partial \ om）\ rightArrow d^{1，p}（\ om）$，是$ t $的右内。
In this paper we fix $1\le p<\infty$ and consider $(\Om,d,μ)$ be an unbounded, locally compact, non-complete metric measure space equipped with a doubling measure $μ$ supporting a $p$-Poincaré inequality such that $\Om$ is a uniform domain in its completion $\bar\Om$. We realize the trace of functions in the Dirichlet-Sobolev space $D^{1,p}(\Om)$ on the boundary $\partial\Om$ as functions in the homogeneous Besov space $HB^α_{p,p}(\partial\Om)$ for suitable $α$; here, $\partial\Om$ is equipped with a non-atomic Borel regular measure $ν$. We show that if $ν$ satisfies a $θ$-codimensional condition with respect to $μ$ for some $0<θ<p$, then there is a bounded linear trace operator $T:D^{1,p}(\Om)\rightarrow HB^{1-θ/p}(\partial\Om)$ and a bounded linear extension operator $E:HB^{1-θ/p}(\partial\Om)\rightarrow D^{1,p}(\Om)$ that is a right-inverse of $T$.
