Xudong Lai

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math.OA2026

Noncommutative Maximal Averages over Submanifolds and Variable Hypersurfaces

Xudong Lai, Siyu Liu

We establish noncommutative maximal inequalities for averages over submanifolds in the $L^{p}$ -spaces associated with semifinite von Neumann algebras. For every $1 < p \leq \infty$ , we p…

math.OA2025

Maximal Riesz transform in terms of Riesz transform on quantum tori and Euclidean space

Xudong Lai, Xiao Xiong, Yue Zhang

For $1 < p < \infty$ , we establish the $L_{p}$ boundedness of the maximal Riesz transforms in terms of the Riesz transforms on quantum tori $L_{p} (T_{θ}^{d})$ , and quantum Eucli…