A Martingale Inequality for the Square and Maximal Functions.

摘要

An inequality for weak martingales and nonnegative weak submartingales is proved. Three special cases are deduced, one of which generalizes and refines a result of Austin (1966). As an application of the inequality, the special cases are used to give easy proofs of Burkholder's (1966) L log L and L sub p (for 1 < p < or = 2) inequalities for the square function of a martingale or a nonnegative submartingale. (Author)