Conditioned square functions for noncommutative martingales

Randrianantoanina, Narcisse

Ann. Probab., Tome 35 (2007) no. 1, p. 1039-1070 / Harvested from Project Euclid

Résumé

We prove a weak-type (1, 1) inequality involving conditioned versions of square functions for martingales in noncommutative L^p-spaces associated with finite von Neumann algebras. As application, we determine the optimal orders for the best constants in the noncommutative Burkholder/Rosenthal inequalities from [Ann. Probab. 31 (2003) 948–995]. We also discuss BMO-norms of sums of noncommuting order-independent operators.

Publié le : 2007-05-14
Classification: Noncommutative L^p-spaces, martingale inequalities, square functions, 46L53, 46L52, 46L51, 60G42

@article{1178804322,
     author = {Randrianantoanina, Narcisse},
     title = {Conditioned square functions for noncommutative martingales},
     journal = {Ann. Probab.},
     volume = {35},
     number = {1},
     year = {2007},
     pages = { 1039-1070},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1178804322}
}

Randrianantoanina, Narcisse. Conditioned square functions for noncommutative martingales. Ann. Probab., Tome 35 (2007) no. 1, pp.  1039-1070. http://gdmltest.u-ga.fr/item/1178804322/