Guixiang Hong

activity

20232025

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4 papers · 1 filter

math.FA2026

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…

math.FA2025

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 $R_{θ}^{d}$ with $θ$ being a $d \times d$ antisymmetric matrix, which is a standard…

math.FA2024

Best constants in the vector-valued Littlewood-Paley-Stein theory

Guixiang Hong, Zhendong Xu, Hao Zhang

Let $L$ be a sectorial operator of type $α$ ( $0 \leq α < π /2$ ) on $L^{2} (R^{d})$ with the kernels of ${e^{- t L}}_{t > 0}$ satisfying certain size and regularity conditions. Defi…

math.FA2023

Operator-Valued Hardy spaces and BMO Spaces on Spaces of Homogeneous Type

Zhijie Fan, Guixiang Hong, Wenhua Wang

Let $M$ be a von Neumann algebra equipped with a normal semifinite faithful trace, $(X, d, μ)$ be a space of homogeneous type in the sense of Coifman and Weiss…