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arXiv · 2610.25339

A noncommutative weak $L_1$-estimate for rough singular integrals

Guixiang Hong·Liang Wang·Xumin Wang·Bang Xu
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Abstract

In this paper, we establish a noncommutative version of Andreas Seeger's weak type $(1,1)$ estimate for singular integral operators with kernels satisfying angular $L\log L$ integrability and an averaged radial Dini condition. The strategy for obtaining the sharp integrability condition involves not only some new estimates of the off-diagonal good and bad functions in Parcet's noncommutative Calderón-Zygmund decomposition but also certain essential modifications of Seeger's kernel decomposition and estimates.

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Guixiang Hong, Liang Wang, Xumin Wang, Bang Xu. 2026-10-18. A noncommutative weak $L_1$-estimate for rough singular integrals. https://arxiv.org/abs/2610.25339

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