Dual spaces for variable martingale Lorentz-Hardy spaces

Let Hp(),q be the variable Lorentz-Hardy martingale spaces. In this paper, we give a new atomic decomposition for these spaces via simple Lr-atoms (1<r <=infinity). Using this atomic decomposition, we consider the dual spaces of variable Lorentz-Hardy spaces Hp(),q for the case 0<p()<= 1, 0<q <= 1, and 0<p()<2, 1<q<infinity respectively, and prove that they are equivalent to the BMO spaces with variable exponent. Furthermore, we also obtain several John-Nirenberg theorems based on the dual results.