26 citations · 61 across the 9 of their papers we have counts for
10 papers
Weyl's laws and Connes' Trace Theorem for operator-valued pseudo-differential operators
Edward McDonald, Xiao Xiong, Xinyu Zhang
We investigate the spectral asymptotic behavior of operator-valued classical pseudo-differential operators (DOs) for negative order with symbols taking values in a semifinite vo…
Twisted Fourier(-Stieltjes) spaces and amenability
Hun Hee Lee, Xiao Xiong
The Fourier(-Stieltjes) algebras on locally compact groups are important commutative Banach algebras in abstract harmonic analysis. In this paper we introduce a generalization of t…
Quantum differentiability on quantum tori
Edward McDonald, Fedor Sukochev, Xiao Xiong
We provide a full characterisation of quantum differentiability (in the sense of Connes) on quantum tori. We also prove a quantum integration formula which differs substantially fr…
Quantum differentiability on noncommutative Euclidean spaces
Edward McDonald, Fedor Sukochev, Xiao Xiong
We study the topic of quantum differentiability on quantum Euclidean -dimensional spaces (otherwise known as Moyal -spaces), and we find conditions that are necessary and suf…
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…
Noncommutative harmonic analysis on semigroup and ultracontractivity
Xiao Xiong
We extend some classical results of Cowling and Meda to the noncommutative setting. Let be a symmetric contraction semigroup on a noncommutative space $L_p(\mathcal{M…
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)…