Anisotropic grand Herz type spaces with variable exponents and their applications

TL;DR

This paper introduces new anisotropic grand Herz type spaces with variable exponents, explores their properties and decompositions, and demonstrates boundedness of certain operators within these spaces.

Contribution

It presents the first study of anisotropic grand Herz spaces with variable exponents and establishes their fundamental properties and operator boundedness.

Findings

Defined anisotropic grand Herz spaces with variable exponents

Established properties and decompositions of these spaces

Proved boundedness of singular integral operators

Abstract

In this paper, we introduce some anisotropic grand Herz type spaces with variable exponents, including anisotropic grand Herz spaces, anisotropic grand Herz-Morrey spaces and anisotropic grand Herz-type Hardy spaces with variable exponents. We obtain some properties and characterizations of these spaces in terms of some decompositions. Using their decompositions, we obtain some boundedness on the anisotropic grand Herz type spaces with variable exponents for some singular integral operators.