25 citations · 109 across the 37 of their papers we have counts for
37 papers
Sharp endpoint estimates of quantum Schrödinger groups
Zhijie Fan, Guixiang Hong, Liang Wang
In this article, we establish sharp endpoint estimates of Schrödinger groups on general measure spaces which may not be equipped with good metrics but admit submarkovian semi…
Quantitative mean ergodic inequalities: power bounded operators acting on one single noncommutative space
Guixiang Hong, Wei Liu, Bang Xu
In this paper, we establish the quantitative mean ergodic theorems for two subclasses of power bounded operators on a fixed noncommutative -space with , which main…
Noncommutative maximal strong estimates of Calderón-Zygmund operators
Guixiang Hong, Xudong Lai, Samya Kumar Ray +1
In this paper, we obtain the desired noncommutative maximal inequalities of the truncated Calderón-Zygmund operators of non-convolution type acting on operator-valued -functio…
Fourier restriction estimates on quantum Euclidean spaces
Guixiang Hong, Xudong Lai, Liang Wang
In this paper, we initiate the study of the Fourier restriction phenomena on quantum Euclidean spaces, and establish the analogues of the Tomas-Stein restriction theorem and the tw…
On Isometric Embeddability of into as non-commutative Quasi-Banach space
Arup Chattopadhyay, Guixiang Hong, Chandan Pradhan +1
The existence of isometric embedding of into , where and has been recently studied in \cite{JFA22}. In this article, we extend…
John-Nirenberg inequalities for noncommutative column BMO and Lipschitz martingales
Guixiang Hong, Congbian Ma, Yu Wang
In this paper, we continue the study of John-Nirenberg theorems for BMO/Lipschitz spaces in the noncommutative martingale setting. As conjectured from the classical case, a desired…
Quantitative ergodic theorems for actions of groups of polynomial growth
Guixiang Hong, Wei Liu
We strengthen the maximal ergodic theorem for actions of groups of polynomial growth to a form involving jump quantity, which is the sharpest result among the family of variational…
Maximal singular integral operators acting on noncommutative -spaces
Guixiang Hong, Xudong Lai, Bang Xu
In this paper, we study the boundedness theory for maximal Calderón-Zygmund operators acting on noncommutative -spaces. Our first result is a criterion for the weak type $(1,1…
Isometric Embeddability of into
Arup Chattopadhyay, Guixiang Hong, Avijit Pal +2
In this paper, we study existence of isometric embedding of into where and We show that for all if ther…
Quantitative weighted bounds for the -variation of singular integrals with rough kernels
Yanping Chen, Guixiang Hong, Ji Li
In this paper, we study the quantitative weighted bounds for the -variational singular integral operators with rough kernels. The main result is for the sharp truncated singular…
Variational Inequalities for Bilinear Averaging Operators over Convex Bodies
Yong Ding, Guixiang Hong, Xinfeng Wu
We study -variation inequality for bilinear averaging operators over convex bodies defined by \begin{align*} \mathbf{A}_t^G(f_1,f_2)(x) & =\frac{1}{|G_t|}\int_{G_t…
Pointwise convergence of noncommutative Fourier series
Guixiang Hong, Simeng Wang, Xumin Wang
This paper is devoted to the study of pointwise convergence of Fourier series for group von Neumann algebras and quantum groups. It is well-known that a number of approximation pro…
Vector-valued -variational inequalities for averaging operators and Hilbert transform
Guixiang Hong, Wei Liu, Tao Ma
Recently, in \cite{GXHTM}, the authors established -boundedness of vector-valued -variational inequalities for averaging operators which take values in the Banach space sat…
An operator-valued theory for symmetric CZOs
Guixiang Hong, Honghai Liu, Tao Mei
We provide a natural BMO-criterion for the -boundedness of Calderón-Zygmund operators with operator-valued kernels satisfying a symmetric property. Our arguments involve both…
Noncommutative weak type estimate for a square function from ergodic theory
Guixiang Hong, Bang Xu
In this paper, we investigate the boundedness of a square function from ergodic theory on noncommutative -spaces. The main result is a weak type estimate of this squ…
Maximal ergodic inequalities for some positive operators on noncommutative -spaces
Guixiang Hong, Samya Kumar Ray, Simeng Wang
In this paper, we establish the one-sided maximal ergodic inequalities for a large subclass of positive operators on noncommutative -spaces for a fixed , which par…
Dimension-free estimates for the vector-valued variational operators
Dan Qing He, Gui Xiang Hong, Wei Liu
In this paper, We study dimension-free estimates for UMD lattice-valued -variations of Hardy-Littlewood averaging operators associated with the Euclidean balls.
Some jump and variational inequalities for the Calderón commutators and related operators
Yanping Chen, Yong Ding, Guixiang Hong +1
In this paper, we establish jump and variational inequalities for the Calderón commutators, which are typical examples of non-convolution Calderón-Zygmund operators. For this purpo…
Variational inequalities for the commutators of rough operators with BMO functions
Yanping Chen, Yong Ding, Guixiang Hong +1
In this paper, starting with a relatively simple observation that the variational estimates of the commutators of the standard Calderón-Zygmund operators with the BMO functions can…
Weighted jump and variational inequalities for rough operators
Yanping Chen, Yong Ding, Guixiang Hong +1
In this paper, we systematically study weighted jump and variational inequalities for rough operators. More precisely, we show some weighted jump and variational inequalities for t…
Noncommutative maximal ergodic inequalities associated with doubling conditions
Guixiang Hong, Ben Liao, Simeng Wang
This paper is devoted to the study of noncommutative maximal inequalities and ergodic theorems for group actions on von Neumann algebras. Consider a locally compact group of po…
Noncommutative ergodic averages of balls and spheres over Euclidean spaces
Guixiang Hong
In this paper, we establish a noncommutative analogue of Calderón's transference principle, which allows us to deduce noncommutative ergodic maximal inequalities from the special c…
Noncommutative maximal ergodic theorems for spherical means on the Heisenberg group
Guixiang Hong
We prove maximal ergodic theorems for spherical averages on the Heisenberg groups acting on spaces over measure spaces not necessarily commutative, that is, on noncommutative…
Asymmetric Doob inequalities in continuous time
Guixiang Hong, Marius Junge, Javier Parcet
The present paper is devoted to the second part of our project on asymmetric maximal inequalities, where we consider martingales in continuous time. Let be a nonco…