12 papers
New matrix-weighted norm inequalities and extrapolation
Guixiang Hong, Pengfei Yin
In this paper, we propose a new type of matrix-weighted theory and show the corresponding Rubio de Francia extrapolation theorems by means of noncommutative maximal inequalities. W…
Vector-valued Littlewood--Paley--Rubio de Francia Inequalities on Vilenkin Systems
Deyu Chen, Guixiang Hong
We investigate two natural formulations of equal-length Littlewood--Paley--Rubio de Francia (LPR) inequalities on arbitrary Vilenkin systems \(\Gm\). The canonical formulation uses…
The weak type estimate of Dirichlet Means for unbounded noncommutative Vilenkin systems
Guixiang Hong, Tiantian Zhao
Let be the hyperfinite factor. Considering the partial sum operators of the noncommutative Vilenkin-Fourier series associa…
Campanato spaces via quantum semigroups
Guixiang Hong, Yuanyuan Jing, Ping Li
In this paper, we continue to investigate Campanato spaces via semigroups on von Neumann algebras. One of the main results is their coincidence with Lipschitz spaces for {\it all}…
Vector-valued partial sums on unbounded Vilenkin systems
Deyu Chen, Guixiang Hong
Let \(\Gm=\prod_{k\ge0}\mathbb Z_{m_k}\) be a Vilenkin group that is not necessarily bounded, i.e., \(\sup_k m_k=\infty\). We prove that, for every UMD Banach space \(X\) and every…
The nonlinear estimates on quantum Besov spaces
Deyu Chen, Guixiang Hong
The superposition operators have been widely studied in nonlinear analysis, which are essential for the well-posedness theory of nonlinear equations. In this paper, we investigate…
Navier-Stokes Equations on Quantum Euclidean Spaces
Deyu Chen, Guixiang Hong, Liang Wang +1
We investigate in the present paper the Navier-Stokes equations on quantum Euclidean spaces with being a antisymmetric matrix, which is a standard…
Noncommutative ergodic theorems for action of semisimple Lie groups
Guixiang hong, Samya Kumar Ray
Let be a connected simple Lie group of real rank one and finite center, and let be a maximal compact subgroup. We study the families of spherical, ball, and uniform average…
Campanato spaces via quantum Markov semigroups on finite von Neumann algebras
Guixiang Hong, Yuanyuan Jing
We study the Campanato spaces associated with quantum Markov semigroups on a finite von Neumann algebra . Let be a Markov semigroup, $\mat…
Best constants in the vector-valued Littlewood-Paley-Stein theory
Guixiang Hong, Zhendong Xu, Hao Zhang
Let be a sectorial operator of type () on with the kernels of satisfying certain size and regularity conditions. Defi…
Operator-Valued Hardy spaces and BMO Spaces on Spaces of Homogeneous Type
Zhijie Fan, Guixiang Hong, Wenhua Wang
Let be a von Neumann algebra equipped with a normal semifinite faithful trace, be a space of homogeneous type in the sense of Coifman and Weiss…
A Representation of Matrix-Valued Harmonic Functions by the Poisson Integral of Non-commutative BMO Functions
Cheng Chen, Guixiang Hong, Wenhua Wang
In this paper, the authors study the matrix-valued harmonic functions and characterize them by the Poisson integral of functions in non-commutative BMO (bounded mean oscillation) s…