3 citations · 6 across the 10 of their papers we have counts for
11 papers
Hilbert transforms on graph products of finite von Neumann algebras
Xiao-Qi Lu, Runlian Xia
We study Hilbert transforms on graph products of finite von Neumann algebras, with particular interests on their boundedness on the associated noncommutative -spaces for $1<p<…
Ergodic Average Dominance for Unimodular Amenable Groups
Ujan Chakraborty, Runlian Xia, Joachim Zacharias
In this paper we show that the ergodic averages of the action of any unimodular amenable group along certain Følner sequences can be dominated by the Cesàro means of a suitably con…
Hilbert transforms on Coxeter groups and groups acting on buildings
Xiao-Qi Lu, Runlian Xia
In this paper, we study Hilbert transforms and their boundedness on -spaces associated with Coxeter groups and groups acting on buildings. We establish new models for Hilbert…
Proper cocycles, measure equivalence and -Fourier multipliers
Simeng Wang, Runlian Xia, Gan Yao
We develop a new transference method for completely bounded -Fourier multipliers via proper cocycles arising from probability measure-preserving group actions. This method ext…
Noncommutative Cotlar identities for groups acting on tree-like structures
Adrian Gonzalez-Perez, Javier Parcet, Runlian Xia
Let be a noncommutative Fourier multiplier. In recent work, Mei and Ricard introduced a noncommutative analogue of Cotlar's identity in order to prove that certain multiplier…
Asymmetric Burkholder inequalities in noncommutative symmetric spaces
Lian Wu, Runlian Xia, Dejian Zhou
In this paper, we establish noncommutative Burkholder inequalities with asymmetric diagonals in symmetric operator spaces. Our proof mainly relies on a new complex interpolation re…
Algebraic Calderón-Zygmund theory
Marius Junge, Tao Mei, Javier Parcet +1
Calderón-Zygmund theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of good metrics, we introduce a new appro…
Mapping properties of operator-valued pseudo-differential operators
Runlian Xia, Xiao Xiong
In this paper, we investigate the mapping properties of pseudo-differential operators with operator-valued symbols. Thanks to the smooth atomic decomposition of the operator-valued…
Operator-valued Triebel-Lizorkin spaces
Runlian Xia, Xiao Xiong
This paper is devoted to the study of operator-valued Triebel-Lizorkin spaces. We develop some Fourier multiplier theorems for square functions as our main tool, and then study the…
Operator-valued local Hardy spaces
Runlian Xia, Xiao Xiong
This paper gives a systematic study of operator-valued local Hardy spaces. These spaces are localizations of the Hardy spaces defined by Tao Mei, and share many properties with Mei…
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…