## The Annals of Probability

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

Maurizio Pratelli

#### 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."

#### Article information

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

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176996409

Digital Object Identifier
doi:10.1214/aop/1176996409

Mathematical Reviews number (MathSciNet)
MR372991

Zentralblatt MATH identifier
0303.60041

JSTOR