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

Abstract

The dual space of B-valued martingale Orlicz-Hardy space H s( p) (B) with a concave function , 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.