Herz-slice spaces and applications

TL;DR

This paper introduces new Herz-slice function spaces, explores their properties, and investigates the boundedness of the Hardy--Littlewood maximal operator within these spaces.

Contribution

It defines homogeneous and non-homogeneous Herz-slice spaces and analyzes the maximal operator's bounds on these novel spaces.

Findings

Defined homogeneous and non-homogeneous Herz-slice spaces.

Established properties of these spaces.

Derived bounds for the Hardy--Littlewood maximal operator.

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 $(\dot KE_{q,r}^{\alpha,p})_t(\mathbb R^n)$, the non-homogeneous Herz-slice space $(KE_{q,r}^{\alpha,p})_t(\mathbb R^n)$ and show some properties of them. As an application, the bounds for the Hardy--Littlewood maximal operator on these spaces is considered.