25 citations · 109 across the 37 of their papers we have counts for
6 papers · 1 filter
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…