On the duality of variable Triebel–Lizorkin spaces

The aim of this paper is to prove the duality of Triebel–Lizorkin spaces F1,q·α·\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ F_{1,q\left( \cdot \right) }^{\alpha \left( \cdot \right) }$$\end{document}. First, we prove the duality of associated sequence spaces. The result follows from the so-called φ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varphi $$\end{document}-transform characterization in the sense of Frazier and Jawerth.