Noncommutative Burkholder/Rosenthal inequalities associated with convex functions

2015/06/12 by Narcisse Randrianantoanina, Randrianantoanina, Narcisse, Lian Wu +1
Mathematics · #46L52 #46L53 #60G42 #FOS: Mathematics #Operator Algebras (math.OA) #Probability (math.PR) #math.OA #math.PR #msc:46L52 #msc:46L53 #msc:60G42

paper · pdf · doi:10.48550/arxiv.1506.04134

arxiv created 2015/06/12 · arxiv updated 2015/06/15

Abstract

We prove noncommutative martingale inequalities associated with convex functions. More precisely, we obtain Φ-moment analogues of the noncommutative Burkholder inequalities and the noncommutative Rosenthal inequalities for any convex Orlicz function Φ whose Matuzewska-Orlicz indices p_Φ and q_Φ are such that 1<p_Φ≤ q_Φ<2 or 2<p_Φ≤ q_Φ<∞. These results generalize the noncommutative Burkholder/Rosenthal inequalities due to Junge and Xu.

Related

• Noncommutative martingale inequalities associated with convex functions
• Johnson-Schechtman inequalities for noncommutative martingales
• Noncommutative maximal inequalities associated with convex functions
• Martingale inequalities in noncommutative symmetric spaces
• Distributional inequalities for noncommutative martingales