167 citations · 538 across the 40 of their papers we have counts for
19 papers · 1 filter
Notes on real interpolation of operator -spaces
Marius Junge, Quanhua Xu
Let be a semifinite von Neumann algebra. We equip the associated noncommutative -spaces with their natural operator space structure introduced by Pisier via comp…
A Hörmander-Mikhlin multiplier theory for free groups and amalgamated free products of von Neumann algebras
Tao Mei, Éric Ricard, Quanhua Xu
We establish a platform to transfer -completely bounded maps on tensor products of von Neumann algebras to -completely bounded maps on the corresponding amalgamated free…
Atomic decompositions for noncommutative martingales
Zeqian Chen, Narcisse Randrianantoanina, Quanhua Xu
We prove an atomic type decomposition for the noncommutative martingale Hardy space $\h_p$ for all by an explicit constructive method using algebraic atoms as building bloc…
Free Fourier Multipliers associated with the firstSegment
Tao Mei, Quanhua Xu
We study Fourier multipliers on free group associated with the first segment of the reduced words, and prove that they are completely bounded on the noncommutat…
Characterizations of operator-valued Hardy spaces and applications to harmonic analysis on quantum tori
Runlian Xia, Xiao Xiong, Quanhua Xu
This paper deals with the operator-valued Hardy spaces introduced and studied by Tao Mei. Our principal result shows that the Poisson kernel in Mei's definition of these spaces can…
Sobolev, Besov and Triebel-Lizorkin spaces on quantum tori
Xiao Xiong, Quanhua Xu, Zhi Yin
This paper gives a systematic study of Sobolev, Besov and Triebel-Lizorkin spaces on a noncommutative -torus (with a skew symmetric real -matrix)…
A noncommutative martingale convexity inequality
Éric Ricard, Quanhua Xu
Let be a von Neumann algebra equipped with a faithful semifinite normal weight and be a von Neumann subalgebra of such that the restri…
A Helson-Szegö theorem for subdiagonal subalgebras with applications to Toeplitz operators
Louis E Labuschagne, Quanhua Xu
We formulate and establish a noncommutative version of the well known Helson-Szego theorem about the angle between past and future for subdiagonal subalgebras. We then proceed to u…
Harmonic analysis on quantum tori
Zeqian Chen, Quanhua Xu, Zhi Yin
This paper is devoted to the study of harmonic analysis on quantum tori. We consider several summation methods on these tori, including the square Fejér means, square and circular…
Complex interpolation of weighted noncommutative -spaces
Éric Ricard, Quanhua Xu
Let be a semifinite von Neumann algebra equipped with a semifinite normal faithful trace . Let be an injective positive measurable operator with respect to $(\…
A reduction method for noncommutative -spaces and applications
Uffe Haagerup, Marius Junge, Quanhua Xu
We consider the reduction of problems on general noncommutative -spaces to the corresponding ones on those associated with finite von Neumann algebras. The main tool is a unpu…
Noncommutative Burkholder/Rosenthal inequalities II: applications
Marius Junge, Quanhua Xu
We show norm estimates for the sum of independent random variables in noncommutative -spaces for following our previous work. These estimates generalize the class…
Riesz and Szegö type factorizations for noncommutative Hardy spaces
Turdebek N. Bekjan, Quanhua Xu
Let $\A$ be a finite subdiagonal algebra in Arveson's sense. Let $H^p(\A)$ be the associated noncommutative Hardy spaces, $0<p\le\8$. We extend to the case of all positive indices…
BMO functions and Carleson measures with values in uniformly convex spaces
Caiheng Ouyang, Quanhua Xu
This paper studies the relationship between vector-valued BMO functions and the Carleson measures defined by their gradients. Let and denote Lebesgue measures on the unit…
Rosenthal type inequalities for free chaos
Marius Junge, Javier Parcet, Quanhua Xu
Let denote the reduced amalgamated free product of a family of von Neumann algebras over a von Neumann subalgebra $\Be…
On the best constants in some non-commutative martingale inequalities
Marius Junge, Quanhua Xu
We determine the optimal orders for the best constants in the non-commutative Burkholder-Gundy, Doob and Stein inequalities obtained recently in the non-commutative martingale theo…
On the maximality of subdiagonal algebras
Quanhua Xu
We consider Arveson's problem on the maximality of subdiagonal algebras. We prove that a subdiagonal algebra is maximal if it is invariant under the modular group of a faithful nor…
Noncommutative maximal ergodic theorems
Marius Junge, Quanhua Xu
This paper is devoted to the study of various maximal ergodic theorems in noncommutative -spaces. In particular, we prove the noncommutative analogue of the classical Dunford-…
Khintchine type inequalities for reduced free products and Applications
Eric Ricard, Quanhua Xu
We prove Khintchine type inequalities for words of a fixed length in a reduced free product of -algebras (or von Neumann algebras). These inequalities imply that the natural p…