标题： 矩阵加权卡姆帕诺空间：对偶性与卡尔德龙-齐格蒙德算子 显示英文标题

标题： Matrix-Weighted Campanato Spaces: Duality and Calderón--Zygmund Operators

摘要： 设$p\in(0,\infty)$,$q\in[1,\infty)$,$s\in\mathbb Z_+$, 和$W$为一个$A_p$-矩阵权，而在标量情况下，这正好是一个 Muckenhoupt$A_{\max\{1,p\}}$权。 在本文中，通过使用$W$的约化算子，我们引入了矩阵加权 Campanato 空间$\mathcal L_{p,q,s,W}$。当$p\in(0,1]$时，利用矩阵加权 Hardy 空间$H^p_W$的原子和有限原子特征，我们证明了$H^p_W$的对偶空间正是$\mathcal L_{p,q,s,W}$，这进一步导出了$\mathcal L_{p,q,s,W}$的几个等价特征。 此外，我们得到了在 $\mathcal L_{p,q,s,W}$ 上带有 $p\in(0,\infty)$ 的修正 Calderón--Zygmund 算子有界的充要条件，该条件结合对偶性，进一步给出了在 $H^p_W$ 上带有 $p\in(0,1]$ 的 Calderón--Zygmund 算子有界的充要条件。 显示英文摘要

摘要： Let $p\in(0,\infty)$, $q\in[1,\infty)$, $s\in\mathbb Z_+$, and $W$ be an $A_p$-matrix weight, which in the scalar case is exactly a Muckenhoupt $A_{\max\{1,p\}}$ weight. In this article, by using the reducing operators of $W$, we introduce matrix-weighted Campanato spaces $\mathcal L_{p,q,s,W}$. When $p\in(0,1]$, applying the atomic and the finite atomic characterizations of the matrix-weighted Hardy space $H^p_W$, we prove that the dual space of $H^p_W$ is precisely $\mathcal L_{p,q,s,W}$, which further induces several equivalent characterizations of $\mathcal L_{p,q,s,W}$. In addition, we obtain a necessary and sufficient condition for the boundedness of modified Calder\'on--Zygmund operators on $\mathcal L_{p,q,s,W}$ with $p\in(0,\infty)$, which, combined with the duality, further gives a necessary and sufficient condition for the boundedness of Calder\'on--Zygmund operators on $H^p_W$ with $p\in(0,1]$.