论文标题
核和紧凑的嵌入在广义平滑度的功能空间中
Nuclear and compact embeddings in function spaces of generalised smoothness
论文作者
论文摘要
我们研究了在有界Lipschitz域上定义的广义平滑度的功能空间$ω\ subset \ mathbb {r}^d $。这尤其涵盖了在有限域上定义的BESOV和Triebel-Lizorkin空间的众所周知的情况，以及对数平滑度的功能空间的一些首先结果。此外，我们还为此类功能空间提供了一些新的，更通用的方法来紧凑型嵌入，这也统一了早期的结果，包括对其熵数的研究。同样，我们依靠合适的小波分解技术和著名的TONT结果（1969年），讲述了在$ \ ell_r $空间中作用的核对角线操作员，我们最近可以将其扩展到这里所需的矢量价值设置。
We study nuclear embeddings for function spaces of generalised smoothness defined on a bounded Lipschitz domain $Ω\subset\mathbb{R}^d$. This covers, in particular, the well-known situation for spaces of Besov and Triebel-Lizorkin spaces defined on bounded domains as well as some first results for function spaces of logarithmic smoothness. In addition, we provide some new, more general approach to compact embeddings for such function spaces, which also unifies earlier results in different settings, including also the study of their entropy numbers. Again we rely on suitable wavelet decomposition techniques and the famous Tong result (1969) about nuclear diagonal operators acting in $\ell_r$ spaces, which we could recently extend to the vector-valued setting needed here.
