Duals of Hardy spaces of B-valued martingales for 0 < r . 1

The dual of B-valued martingale Hardy space H s(p)r(B) with small index 0 < r . 1, which is associated with the conditional p-variation of B-valued martingale, is characterized. In order to obtain the results, a new type of Campanato spaces for B-valued martingales is introduced and the classical technique of atomic decompositions is improved. Some results obtained here are connected closely with the p-uniform smoothness and q-uniform convexity of the underlying Banach space.