论文标题
可实现的特征及其对矩阵加权的Triebel- lizorkin空间的应用
Real-Variable Characterizations and Their Applications of Matrix-Weighted Triebel--Lizorkin Spaces
论文作者
论文摘要
Let $α\in\mathbb R$, $q\in(0,\infty]$, $p\in(0,\infty)$, and $W$ be an $A_p(\mathbb{R}^n,\mathbb{C}^m)$-matrix weight. In this article, the authors characterize the matrix-weighted Triebel-Lizorkin space $ \ dot {f} _ {p}^{α，q}（w）$通过PEETRE最大功能，Lusin区域功能和Littlewood-Paley $G_λ^{**} $ - 作为应用程序，作者在Mattrix-Weighteded triebel-lmmork上建立了傅立叶多级 novelty of these results exists in that their proofs need to fully use both the doubling property of matrix weights and the reducing operator associated to matrix weights, which are essentially different from those proofs of the corresponding cases of classical Triebel-Lizorkin spaces that strongly depend on the Fefferman-Stein vector-valued maximal inequality on Lebesgue spaces.
Let $α\in\mathbb R$, $q\in(0,\infty]$, $p\in(0,\infty)$, and $W$ be an $A_p(\mathbb{R}^n,\mathbb{C}^m)$-matrix weight. In this article, the authors characterize the matrix-weighted Triebel-Lizorkin space $\dot{F}_{p}^{α,q}(W)$ via the Peetre maximal function, the Lusin area function, and the Littlewood-Paley $g_λ^{*}$-function. As applications, the authors establish the boundedness of Fourier multipliers on matrix-weighted Triebel-Lizorkin spaces under the generalized Hörmander condition. The main novelty of these results exists in that their proofs need to fully use both the doubling property of matrix weights and the reducing operator associated to matrix weights, which are essentially different from those proofs of the corresponding cases of classical Triebel-Lizorkin spaces that strongly depend on the Fefferman-Stein vector-valued maximal inequality on Lebesgue spaces.
