Dual spaces of weak Orlicz–Hardy spaces for vector-valued martingales

Abstract

The dual spaces of weak Orlicz–Hardy spaces for B-valued martingales, which are defined by quasi-concave functions, are identified. To obtain the results, the so-called weak-type generalized Campanato spaces are introduced and the classical technique of atomic decompositions is employed. The results obtained here extend the corresponding known results in the literature from real-valued setting to vector-valued setting and from strong-type spaces to weak-type spaces.