Weak Atomic Decompositions of Weak Orlicz Martingale Spaces and Applications

摘要

In this paper, weak atomic decompositions of three kinds of weak Orlicz martingale spaces generated by concave functions are established. As applications, the author first gives a sufficient condition for a sublinear operator to be bounded on weak Orlicz martingale spaces, and based on this, some weak-type martingale inequalities are proved. Then, the author proves a Marcinkiewicz-type interpolation theorem for weak Orlicz martingale spaces.