Noncommutative Burkholder/Rosenthal inequalities

By Marius Junge, Quanhua Xu. 2003

267 citations recorded by the source corpus.

Subfields: Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/96046c1401863bd9de89d544a8dbd5ecfa36175e

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Citations in the corpus

Noncommutative Burkholder/Rosenthal inequalities II: Applications (2007, methodology): “,Ak), we see that (Mk) is an increasing filtration of subalgebras in the sense of [JX1], which yields a noncommutative martingale structure in M.”
Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori (2015, background): “Motivated by the developments of noncommutative martingale inequalities in [56, 36] and quantum Markovian semigroups in [32], Mei [44] developed the theory of operator-valued Hardy spaces on R.”
Noncommutative Boyd interpolation theorems (2012, methodology): “Our results extend the Burkholder-Gundy and Rosenthal inequalities established in [7], as well as the Burkholder-Rosenthal inequalities for noncommutative L-spaces and Lorentz spaces obtained in [18] and [15], respectively.”
A Weak Type Inequality for Non‐Commutative Martingales and Applications (2004, methodology): “For the next application, we recall the dual space of H (1 < p < 2) studied in [25].”
Pseudo-localization of singular integrals and noncommutative Calderon-Zygmund theory (2007, background): “ncommutative setting. A noncommutative analogue of Doob’s maximal function [24], the noncommutative John-Nirenberg theorem [26], extensions of Burkholder inequalities for conditioned square functions [30] and related weak type inequalities [50, 51, 52]; see [44] for a simpler approach to some of the”
Noncommutative Riesz transforms -- a probabilistic approach (2008, methodology): “The notation supn + is taken from [Jun02] and [JX03].”
Noncommutative Riesz transforms -- Dimension free bounds and Fourier multipliers (2014, background): “ M is fully independent overEif the von Neumann algebrasgenerated by any two disjoint subsets of (fj)j∈J are independent over E. The noncommutative analog of Rosenthal inequality [58] was obtained in [37] and read as follows for p≥ 2. If the random variables (fj)j∈J ⊂ Lp(M) satisfy E(fj) = 0 and are”
A reduction method for noncommutative L_p-spaces and applications (2008, methodology): “These inequalities were proved in [PX1] for the tracial case and in [JX1] for the general case.”
On the Best Constants in Some Non‐Commutative Martingale Inequalities (2005, methodology): “We refer to [9] for the known constants in the Burkholder and Rosenthal inequalities.”
Noncommutative maximal ergodic theorems (2005, background): “e regarded naturally and isometrically as subspaces of Lp(R). Moreover, the conditional expectation Φ (resp. Φm) extends to a positive contractive projection from Lp(R) onto Lp(M) (resp. Lp(Rm)) (see [JX2]; this is also a particular case of Lemma 7.1). On the other hand, S m≥1 Lp(Rm) is dense in Lp(”
Smooth Fourier multipliers on group von Neumann algebras (2010, background): “⋊G = 1 √ m Xm j=1 X h,g B(h⊗ej) ⊗fg,h λ(g) p . SMOOTH MULTIPLIERS ON GROUP VON NEUMANN ALGEBRAS 29 We may deﬁne the random variables fj = P h,g(B(h⊗ ej) ⊗ fg,h)λ(g), which are independent over E, see [30, 32] for details. Hence, the noncommutative Rosenthal inequality applies and we have kfkG p(M)⋊G”
The Masked Sample Covariance Estimator: An Analysis via Matrix Concentration Inequalities (2011, background): “This literature contains many powerful moment bounds that can also be used to study sums of independent random matrices [19–22].”
$H^{\infty }$ functional calculus and square functions on noncommutative $L^p$-spaces (2006, background): “See in particular [66, 33, 70, 37], and also the recent survey [81] and the references therein.”
Pseudo-Localization of Singular Integrals and Noncommutative Littlewood–Paley Inequalities (2008, background): “oncommutative setting. A noncommutative analogue of Doob’s maximal function [8], the noncommutative John-Nirenberg theorem [11], extensions of Burkholder inequalities for conditioned square functions [15] and related weak type inequalities [29, 30]; see [26] for a simpler approach to some of them. A”