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

Abstract

In this paper, we identify the dual spaces of variable Dunkl--Hardy spaces using a discrete Dunkl--Calderón reproducing formula and the Frazier and Jawerth's method adapted to the variable exponent setting. Furthermore, we prove a $T1$ theorem for Dunkl--Calderón--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.

20 pages