  In this paper, several weak Orlicz-Hardy martingale spaces associated with
concave functions are introduced, and some weak atomic decomposition theorems
for them are established. With the help of weak atomic decompositions, a
sufficient condition for a sublinear operator defined on the weak Orlicz-Hardy
martingale spaces to be bounded is given. Further, we investigate the duality
of weak Orlicz-Hardy martingale spaces and obtain a new John-Nirenberg type
inequality when the stochastic basis is regular. These results can be regarded
as weak versions of the Orlicz-Hardy martingale spaces due to Miyamoto, Nakai
and Sadasue.
