分形h-集上Besov空间的迹及二分性结果
Traces for Besov spaces on fractal h-sets and dichotomy results
摘要：
我们研究了分形$h$ -集$Γ$上Besov空间迹的存在性，特别着重于暗示这种存在性的必要假设，或者换句话说，给出迹不存在的准则。从这个意义上说，我们的文件可以被视为[Br 4]的扩展和最近的文件[Ca 2]的继续。与迹的存在性问题密切相关的是函数空间中的二分法的概念：我们可以证明--取决于函数空间和集合$Γ$ --存在一种替代：要么在$Γ$上存在迹，要么在$Γ$之外紧支持的光滑函数在空间中是稠密的。这个概念是Triebel在[Tr 7]中为$d$ -集的特殊情况引入的。
英文摘要：
We study the existence of traces of Besov spaces on fractal $h$-sets $Γ$ with the special focus laid on necessary assumptions implying this existence, or, in other words, present criteria for the non-existence of traces. In that sense our paper can be regarded as an extension of [Br4] and a continuation of the recent paper [Ca2]. Closely connected with the problem of existence of traces is the notion of dichotomy in function spaces: We can prove that -- depending on the function space and the set $Γ$ -- there occurs an alternative: either the trace on $Γ$ exists, or smooth functions compactly supported outside $Γ$ are dense in the space. This notion was introduced by Triebel in [Tr7] for the special case of $d$-sets.
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