Herz-slice spaces and applications

Abstract

Let $\alpha \in {\mathbb{R}}^n$, $t\in (0,\infty )$, $p\in (0,\infty ]$, $r\in (1,\infty )$ and $q\in [1,\infty ]$. We introduce the homogeneous Herz-slice space $(\dot{K}{E}_{q,r}^{\alpha ,p}{)}_t({\mathbb{R}}^n)$, the non-homogeneous Herz-slice space $(K{E}_{q,r}^{\alpha ,p}{)}_t({\mathbb{R}}^n)$ and show some properties of them. As an application, the bounds for the Hardy--Littlewood maximal operator on these spaces is considered.

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