论文标题
各向异性Triebel-lizorkin空间的分类
Classification of anisotropic Triebel-Lizorkin spaces
论文作者
论文摘要
本文提供了用于扩展矩阵$ a \ in \ mathrm {gl}（d，\ mathbb {r}）$生成相同的各向异性均质triebel-lizorkin空间$ \ dot $ \ dot $ \ dot {\ mathbf {f}}^^p，p， \ Mathbb {r} $和$ p，q \ in（0，\ infty] $。显示出$ \ dot {\ mathbf {f}}^α__{p，q}（a）= \ dot { $ρ_a，ρ_b$与矩阵$ a，b $相关，除了情况外，$ \ dot {\ mathbf {f}}^0_ {p，2} = l^p $与$ p \ in（1，\ infty）$ p \ in（1，\ infty）$。 \ dot {\ mathbf {f}}}^{0} _ {p，2}（a）$，$ p \ in（0,1] $，in [mem。Am。Math。Soc。781，122 p。（2003）]。
This paper provides a classification theorem for expansive matrices $A \in \mathrm{GL}(d, \mathbb{R})$ generating the same anisotropic homogeneous Triebel-Lizorkin space $\dot{\mathbf{F}}^α_{p, q}(A)$ for $α\in \mathbb{R}$ and $p,q \in (0,\infty]$. It is shown that $\dot{\mathbf{F}}^α_{p, q}(A) = \dot{\mathbf{F}}^α_{p, q}(B)$ if and only if the homogeneous quasi-norms $ρ_A, ρ_B$ associated to the matrices $A, B$ are equivalent, except for the case $\dot{\mathbf{F}}^0_{p, 2} = L^p$ with $p \in (1,\infty)$. The obtained results complement and extend the classification of anisotropic Hardy spaces $H^p(A) = \dot{\mathbf{F}}^{0}_{p,2}(A)$, $p \in (0,1]$, in [Mem. Am. Math. Soc. 781, 122 p. (2003)].
