Dual spaces and T1 theorem of variable Dunkl--Hardy spaces

In this paper, we identify the dual spaces of variable Dunkl–Hardy spaces using a discrete Dunkl–Calder'on reproducing formula and the Frazier and Jawerth’s method adapted to the variable exponent setting. Furthermore, we prove a $T1$ theorem for Dunkl–Calder'on–Zygmund operators acting on variable Dunkl–Hardy spaces and on their dual spaces via using almost orthogonal estimate, the duality result and the density argument.