Abstract
In this paper, the weak Orlicz space wL Φ is introduced and its applications to the martingale theory are discussed. In particular, a series of martingale inequalities including the maximal function inequality in weak Orlicz spaces are established; the relationships between these spaces are investigated. Moreover, the boundedness of several sublinear operators from one weak Orlicz space to another is proved; their vector-valued analogues are also considered.
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