Square function inequalities for non-commutative martingales
This paper is the second one of a series of three papers by the author on noncommutative martingale inequalities. In the present paper, the author continues his study of weak type (1,1) inequalities for noncommutative martingales. Using the method developed in his first paper [J. Funct. Anal. 194, 181--212 (2002; Zbl 1030.46083)], he obtains a noncommutative version of the classical Burkholder weak type (1,1) inequality for the martingale square function. However, this noncommutative weak type (1,1) inequality is not very satisfactory, for the two sequences in the decomposition of a given martingale difference sequence are not formed of martingale differences. This problem has been solved in the author's third paper that will appear in Bull. Lond. Math. Soc.
scientific article; zbMATH DE number 2114406
scientific article