Abstract
In this paper the following two theorems are shown: if $U, V$ are Burkholder type operators on martingales and if the inequality $E\lbrack U(X) \rbrack \leqq c \cdot E\lbrack V(X) \rbrack$ holds for every martingale $X$, then the inequality $E\lbrack F \circ U(X) \rbrack \leqq C \cdot E\lbrack F \circ V(X) \rbrack$ holds, for $F$ concave if $V$ is "predictable," for $F$ convex if $U$ is "predictable."
Citation
Maurizio Pratelli. "Deux Inegalites Concernant Les Operateurs de Burkholder Sur Les Martingales." Ann. Probab. 3 (2) 365 - 370, April, 1975. https://doi.org/10.1214/aop/1176996409
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