On the duality of variable Triebel-Lizorkin spaces

The aim of this paper is to prove the duality of Triebel-Lizorkin spaces F1,qmml:mfenced close=")" open="("center dot alpha mml:mfenced close=")" open="("center dot$$ F_{1,q\left( \cdot \right) }<<^>>{\alpha \left( \cdot \right) }$$\end{document}. First, we prove the duality of associated sequence spaces. The result follows from the so-called phi\-transform characterization in the sense of Frazier and Jawerth.