论文标题
均匀混合符号Triebel-lizorkin空间的稳定分解
Stable decomposition of homogeneous Mixed-norm Triebel-Lizorkin spaces
论文作者
论文摘要
我们在$ \ br^d $上的各向异性环境中构建了与均匀的混合 - 荷兰 - 荷兰金素空间兼容的平滑局部正常基碱。该结构基于所谓的单变量刷子功能的张量产品，这些函数是使用频域中局部三角碱构建的。结果表明，相关的分解系统构成了均质混合符号Triebel-lizorkin空间的无条件碱基。 在本文的第二部分中，我们研究了非线性$ m $ - 期非线性近似，并在混合声明环境中构建基础，通常，这种行为通常以$ d \ geq 2 $为基础，与未混合情况根本不同。但是，仍然可以得出杰克逊和伯恩斯坦的不平等现象。
We construct smooth localized orthonormal bases compatible with homogeneous mixed-norm Triebel-Lizorkin spaces in an anisotropic setting on $\bR^d$. The construction is based on tensor products of so-called univariate brushlet functions that are constructed using local trigonometric bases in the frequency domain. It is shown that the associated decomposition system form unconditional bases for the homogeneous mixed-norm Triebel-Lizorkin spaces. In the second part of the paper we study nonlinear $m$-term nonlinear approximation with the constructed basis in the mixed-norm setting, where the behaviour, in general, for $d\geq 2$, is shown to be fundamentally different from the unmixed case. However, Jackson and Bernstein inequalities for $m$-term approximation can still be derived.
