论文标题
在半线上定义的加权dirichlet空间的渐近学，痕量和密度结果
Asymptotics, trace, and density results for weighted Dirichlet spaces defined on the halfline
论文作者
论文摘要
我们给出了$ C_0^\ Infty（\ MathBf {r} _+）$完成的分析说明$ d^{1，p}（\ Mathbf {r} _+，ω）：= \ \ \ {u {连续ON} \ \ Mathbf {r} _+ \ {\ rm and} \ \ | u^{'} \ | _ {l^p（\ mathbf {r} _+，ω）} <\ infty \} $，对于给定的连续权重$ω$，就本地$ b_p $而言，kufner和opic所致，其中$ 1 <p <\\ iffty $。此外，我们提出了结果的应用：分析强硬不平等，边界价值问题，复杂的插值理论以及新的莫雷类型不平等的推导。
We give analytic description for the completion of $C_0^\infty ( \mathbf{R}_+)$ in Dirichlet space $D^{1,p}(\mathbf{R}_+, ω):= \{ u:\mathbf{R}_+\rightarrow \mathbf{R}: u\ \hbox{ is locally absolutely continuous on} \ \mathbf{R}_+ \ {\rm and}\ \| u^{'}\|_{L^p(\mathbf{R}_+, ω)}<\infty \}$, for given continuous weight $ω$, in terms of the local $B_p$ conditions due to Kufner and Opic, where $1<p<\infty$. Moreover, we propose applications of our results to: analysis of Hardy inequalities, boundary value problems, complex interpolation theory, and to derivation of new Morrey type inequalities.
