6 papers · 1 filter
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…