Martingale Orlicz‐Hardy spaces

The purpose of this paper is to introduce five martingale Orlicz‐Hardy spaces and to establish the atomic decomposition theorem. As applications we show the relation among five martingale Orlicz‐Hardy spaces and the duality, namely, the dual of martingale Orlicz‐Hardy spaces are generalized martingale Campanato spaces. Further, we prove a John‐Nirenberg type inequality for generalized martingale Campanato spaces when the stochastic basis is regular.