The Weighted Grand Herz-Morrey-Lizorkin-Triebel Spaces with Variable Exponents

TL;DR

This paper introduces and analyzes weighted grand Herz-Morrey-Triebel-Lizorkin spaces with variable exponents, establishing boundedness of certain operators and providing equivalent quasi-norms via maximal functions.

Contribution

It extends the theory of function spaces by defining new weighted grand Herz-Morrey-Triebel-Lizorkin spaces with variable exponents and characterizes their quasi-norms.

Findings

Boundedness of vector-valued sublinear operators on these spaces.

Equivalent quasi-norms via maximal functions are established.

The framework generalizes classical spaces with variable exponents.

Abstract

Let a vector-valued sublinear operator satisfy the size condition and be bounded on weighted Lebesgue spaces with variable exponent. Then we obtain its boundedness on weighted grand Herz-Morrey spaces with variable exponents. Next we introduce weighted grand Herz-Morrey-Triebel-Lizorkin spaces with variable exponents and provide their equivalent quasi-norms via maximal functions.