4 papers
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…
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…