On the duality of variable Triebel-Lizorkin spaces

TL;DR

This paper establishes the duality of variable Triebel-Lizorkin spaces by proving duality of related sequence spaces and utilizing the $\

Contribution

It introduces a novel proof of duality for variable Triebel-Lizorkin spaces using sequence space duality and $\\varphi$-transform characterization.

Findings

Duality of associated sequence spaces proved.

Main duality result derived from $\\varphi$-transform characterization.

Provides a foundation for further analysis of variable function spaces.

Abstract

The aim of this paper is to prove duality of Triebel-Lizorkin spaces $% F_{1,q\left( \cdot \right) }^{\alpha \left( \cdot \right) }$. First, we prove the duality of associated sequence spaces. Then from the so-called $% \varphi $-transform characterization in the sense of Frazier and Jawerth, we deduce the main result of this paper.