167 citations · 538 across the 40 of their papers we have counts for
15 papers · 1 filter
Holomorphic functional calculus and vector-valued Littlewood-Paley-Stein theory for semigroups
Quanhua Xu
We study vector-valued Littlewood-Paley-Stein theory for semigroups of regular contractions on for a fixed . We prove that if a Banach space $X…
Vector-valued Littewood-Paley-Stein theory for semigroups II
Quanhua Xu
Inspired by a recent work of Hytönen and Naor, we solve a problem left open in our previous work joint with Mart\'ınez and Torrea on the vector-valued Littlewood-Paley-Stein theory…
functional calculus and maximal inequalities for semigroups of contractions on vector-valued -spaces
Quanhua Xu
Let be a strongly continuous semigroup of positive contractions on with . Let be a UMD Banach lattice of measurable functions on another…
Fractional Vector-Valued Littlewood-Paley-Stein Theory for Semigroups
José L. Torrea, Chao Zhang
We consider the fractional derivative of a general Poisson semigroup. With this fractional derivative we define the generalized fractional Littlewood-Paley -function for semigro…
On the vector-valued Littlewood-Paley-Rubio de Francia inequality
Denis Potapov, Fedor Sukochev, Quanhua Xu
The paper studies Banach spaces satisfying the Littlewood-Paley-Rubio de Francia property LPR_p, 2 \leq p < \infty. The paper shows that every Banach lattice whose 2-concavificatio…
Maximal theorems and square functions for analytic operators on Lp-spaces
Christian Le Merdy, Quanhua Xu
Let T : Lp --> Lp be a contraction, with p strictly between 1 and infinity, and assume that T is analytic, that is, there exists a constant K such that n\norm{T^n-T^{n-1}} < K for…
Representation of certain homogeneous Hilbertian operator spaces and applications
Marius Junge, Quanhua Xu
Following Grothendieck's characterization of Hilbert spaces we consider operator spaces such that both and completely embed into the dual of a C*-algebra. Due to Haag…
Counterexamples for the convexity of certain matricial inequalities
Marius Junge, Quanhua Xu
This paper is withdrawn. We found a mistake in Lemma 4.1
The little Grothendieck theorem and Khintchine inequalities for symmetric spaces of measurable operators
Françoise Lust-Piquard, Quanhua Xu
We prove the little Grothendieck theorem for any 2-convex noncommutative symmetric space. Let $\M$ be a von Neumann algebra equipped with a normal faithful semifinite trace $\t$, a…
functional calculus and square functions on noncommutative -spaces
Marius Junge, Christian Le Merdy, Quanhua Xu
In this work we investigate semigroups of operators acting on noncommutative -spaces. We introduce noncommutative square functions and their connection to sectoriality, varian…
Embedding of and into noncommutative -spaces,
Quanhua Xu
We prove that a quotient of subspace of () embeds completely isomorphically into a noncommutative -space, where and are respectively the…
Operator space Grothendieck inequalities for noncommutative -spaces
Quanhua Xu
We prove the operator space Grothendieck inequality for bilinear forms on subspaces of noncommutative -spaces with . One of our results states that given a map $u:…
A description of
Quanhua Xu
We give a simple explicit description of the norm in the complex interpolation space for any von Neumann algebra and any .
On subspaces of non-commutative L_p-spaces
Yves Raynaud, Quanhua Xu
We study some structural aspects of the subspaces of the non-commutative (Haagerup) L_p-spaces associated with a general (non necessarily semi-finite) von Neumann algebra A. If a s…
Non-commutative martingale inequalities
Gilles Pisier, Quanhua Xu
We prove the analogue of the classical Burkholder-Gundy inequalites for non-commutative martingales. As applications we give a characterization for an Ito-Clifford integral to be a…