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Weak martingale hardy spaces

Weisz F.

Probability and Mathematical Statistics

1998

Vol. 18, Fasc. 1

133--148

Weak martingale Hardy spaces generated by an operator T are investigated. The concept of weak atoms is introduced and an atomic decomposition of the space wHTp is given if the operator T is predictable. Martingale inequalities between weak Hardy spaces generated by two different operators are considered. In particular, we obtain inequalities for the maximal function, for the q-variation, and for the conditional q-variation. The duals of the weak Hardy spaces generated by these special operators are characterized.