Grand variable Herz-Morrey type Besove spaces and Triebel-Lizorkin spaces

TL;DR

This paper investigates the boundedness of vector-valued operators in new grand variable Herz-Morrey spaces and introduces related Besov and Triebel-Lizorkin spaces with equivalent quasi-norms.

Contribution

It defines grand variable Herz-Morrey type Besov and Triebel-Lizorkin spaces and establishes their properties, including equivalent quasi-norms via Peetre's maximal operators.

Findings

Boundedness of vector-valued sublinear operators in these spaces

Definition of grand variable Herz-Morrey type Besov and Triebel-Lizorkin spaces

Equivalence of quasi-norms using Peetre's maximal operators

Abstract

In the article, the boundedness of vector-valued sublinear operators in grand variable Herz-Morrey spaces $M \dot{K}_{ \lambda, p(\cdot)}^{\eta (\cdot), q), \theta}\left(\mathbb{R}^{n}\right)$ are obtained. Then grand variable Herz-Morrey type Besov and Triebel-Lizorkin spaces are defined. We will also prove the equivalent quasi-norms by Peetre's maximal operators in these spaces.