Conditioned square functions for noncommutative martingales

By Narcisse Randrianantoanina. 2005

76 citations recorded by the source corpus.

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.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/066a612d92d04ae0898e7e6206a7ff102d99c7ea

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In Applied Mathematics

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Citations in the corpus

Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory (2007, methodology): “ proved in [9] the noncommutative Doob’s maximal weak type inequality. Moreover, these techniques were used by Randrianantoanina to prove several weak type inequalities for noncommutative martingales [50, 51, 52] and by Junge and Xu in their remarkable paper [31]. In fact, a strong motivation for th”
Noncommutative martingale deviation and Poincaré type inequalities with applications (2012, background): “The optimal order of constant here is c(p) ∼ cp in the noncommutative setting, and is due to Randrianantoanina [50].”
Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori (2015, background): “[17] was made possible by the recent developments on noncommutative martingale/ergodic inequalities and the Littlewood-Paley-Stein theory for quantum Markovian semigroups, which had been achieved thanks to the efforts of many researchers; see, for instance, [56, 31, 36, 37, 61, 62, 52], and [32, 44,”
Noncommutative Bennett and Rosenthal inequalities (2011, background): “The martingale situation is completely settled due to the work of [32] which shows that for noncommutative martingales”
A reduction method for noncommutative L_p-spaces and applications (2008, background): “The estimates on ηp and ζp mainly come from [R3], although some partial results already appeared in [JX1] and [JX3].”
Rosenthal inequalities in noncommutative symmetric spaces (2011, methodology): “As a result we obtain a new proof of Rosenthal’s theorem for (Haagerup) Lp-spaces.”