Herz-slice spaces and applications

Let $α\in\mathbb R^n$, $t\in(0,\infty)$, $p\in(0,\infty]$, $r\in(1,\infty)$ and $q\in[1,\infty]$. We introduce the homogeneous Herz-slice space $(\dot KE_{q,r}^{α,p})_t(\mathbb R^n)$, the non-homogeneous Herz-slice space $(KE_{q,r}^{α,p})_t(\mathbb R^n)$ 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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