arXiv:2610.33284v1 Announce Type: new Abstract: We prove a weak type $(1,1)$ estimate for maximal truncations of noncommutative rough singular integrals whose angular kernels satisfy the classical $L\log L$ integrability and cancellation conditions. The main ingredient of the proof is a new linearization method for handling the maximal truncations acting on the bad functions arising from the noncommutative Calder\'on--Zygmund decomposition.
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