Duality theorem for B ‐valued martingale Orlicz–Hardy spaces associated with concave functions

The dual space of B ‐valued martingale Orlicz–Hardy spaceH Φ s ( p )( B )with a concave function Φ, which is associated with the conditional p ‐variation of B ‐valued martingale, is characterized. 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.