3 papers
math.FA2026
Noncommutative weak type estimates for Calderón-Zygmund operators with a class of -integral conditions
Xudong Lai, Lingxin Xu
We construct a slightly new noncommutative Calderón-Zygmund decomposition by further splitting the bad function. Using this tool, we prove the weak type (1,1) boundedness of nonco…
math.CA2025
Weak estimate for maximal truncated rough singular integral operator
Xudong Lai
In their seminal work (Amer. J. Math. 78: 289-309, 1956), Calderón and Zygmund introduced the maximal truncated rough singular integral operator and established its -boundedn…
math.FA2025
Noncommutative Bourgain's circular maximal theorem and a local smoothing estimate on the generalized Moyal planes
Guixiang Hong, Xudong Lai, Liang Wang
In this paper, we establish a local smoothing estimate on two-dimensional quantum Euclidean space. This is the noncommutative analogue of the one due to MockenhauptSeegerSogg…