### Deux Inegalites Concernant Les Operateurs de Burkholder Sur Les Martingales

Maurizio Pratelli
Source: Ann. Probab. Volume 3, Number 2 (1975), 365-370.

#### 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."

First Page:
Primary Subjects: 60G45
Secondary Subjects: 47H99
Full-text: Open access