论文标题
加权功能空间中的核嵌入
Nuclear embeddings in weighted function spaces
论文作者
论文摘要
我们研究BESOV和Triebel-lizorkin型的加权空间的核嵌入，其中权重属于某些粉碎型类别，并且本质上是多项式类型的。在这里，我们可以扩展先前的结果[17,19]，在其中研究了相应嵌入的紧凑性。核性的概念可以追溯到格罗伦迪克（Grothendieck），后者在[14]中定义了它。最近，研究此类问题引起了人们的兴趣[5-8,49]。这使我们在加权环境中进行了调查。我们获得了相应嵌入的核性的完整特征。基本工具是在小波基础，操作员理想技术方面的离散化，也是TONG [43]的非常有用的结果，内容涉及在$ \ ell_p $空间中作用的对角线操作员的核性。这样，我们可以进一步促进[5,33,34,49]中获得的核嵌入的表征。
We study nuclear embeddings for weighted spaces of Besov and Triebel-Lizorkin type where the weight belongs to some Muckenhoupt class and is essentially of polynomial type. Here we can extend our previous results [17,19] where we studied the compactness of corresponding embeddings. The concept of nuclearity goes back to Grothendieck who defined it in [14]. Recently there is a refreshed interest to study such questions [5-8,49]. This led us to the investigation in the weighted setting. We obtain complete characterisations for the nuclearity of the corresponding embedding. Essential tools are a discretisation in terms of wavelet bases, operator ideal techniques, as well as a very useful result of Tong [43] about the nuclearity of diagonal operators acting in $\ell_p$ spaces. In that way we can further contribute to the characterisation of nuclear embeddings on domains obtained in [5,33,34,49].
