## The Annals of Probability

### A Martingale Inequality for the Square and Maximal Functions

Louis H. Y. Chen

#### Abstract

An inequality for certain random sequences more general than martingales or nonnegative submartingales is proved. Three special cases are deduced, one of which generalizes and refines a result of Austin. As an application of the inequality, the special cases are used to give new proofs of Burkholder's $L \log L$ and $L_p$ (for $1 < p \leqslant 2$) inequalities for the square function of a martingale or a nonnegative submartingale.

#### Article information

Source
Ann. Probab., Volume 7, Number 6 (1979), 1051-1055.

Dates
First available in Project Euclid: 19 April 2007

https://projecteuclid.org/euclid.aop/1176994898

Digital Object Identifier
doi:10.1214/aop/1176994898

Mathematical Reviews number (MathSciNet)
MR548899

Zentralblatt MATH identifier
0421.60039

JSTOR