  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.
