论文标题
HERZ型空间上的操作员与球级准 - 巴纳赫功能空间相关
Operators on Herz-type spaces associated with ball quasi-Banach function spaces
论文作者
论文摘要
令$α\ in {\ bbb r} $，$ 0 <p <\ infty $和$ x $是$ {\ bbb r}^n $上的球准巴纳赫功能空间。在本文中，我们介绍了HERZ型空间$ \ dot {k}^{α，p} _x（{\ bbb r}^n）$与$ x $相关。我们确定$ \ dot {k}^{α，p} _x（{\ bbb r}^n）$的双空间，通过该$ \ dot {k}^{k}^{α，p} _x（\ bb r}^n）$ \ dot {k}^{k}^{k}^{k}^{通过在Ball Quasi-Banach函数空间上使用推断定理，我们在与Ball Quasi-Banach函数空间相关的HERZ型空间上建立了推断定理。应用我们的外推理，与粗糙内核及其换向器的奇异积分运算符的界限，参数Marcinkiewicz积分以及振荡性的单数积分运算符在$ \ dot {k}^{k}^{α，p} _x _x（{\ bbb r}^n）$上。作为示例，我们提供了一些混凝土函数空间，这些空间是与球级准 - 巴纳赫功能空间相关的HERZ型空间的成员。
Let $α\in{\Bbb R}$, $0<p<\infty$ and $X$ be a ball quasi-Banach function space on ${\Bbb R}^n$. In this article, we introduce the Herz-type space $\dot{K}^{α,p}_X({\Bbb R}^n)$ associated with $X$. We identify the dual space of $\dot{K}^{α,p}_X({\Bbb R}^n)$, by which the boundedness of Hardy-Littlewood maximal operator on $\dot{K}^{α,p}_X({\Bbb R}^n)$ is proved. By using the extrapolation theorem on ball quasi-Banach function spaces, we establish the extrapolation theorem on Herz-type spaces associated with ball quasi-Banach function spaces. Applying our extrapolation theorem, the boundedness of singular integral operators with rough kernels and their commutators, parametric Marcinkiewicz integrals, and oscillatory singular integral operators on $\dot{K}^{α,p}_X({\Bbb R}^n)$ is obtained. As examples, we give some concrete function spaces which are members of Herz-type spaces associated with ball quasi-Banach function spaces.
