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Weak type (1,1) estimates for noncommutative maximal truncated rough singular integrals
Abstract
We prove a weak type (1,1) estimate for maximal truncations of noncommutative rough singular integrals whose angular kernels satisfy the classical Llog 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 Calderón--Zygmund decomposition.
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BibTeX
@misc{cao2026weak,
title = {{Weak type $(1,1)$ estimates for noncommutative maximal truncated rough singular integrals}},
author = {Junming Cao and Wei Li},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.33284},
eprint = {2610.33284},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.33284},
}
RIS
TY - UNPB
TI - Weak type (1,1) estimates for noncommutative maximal truncated rough singular integrals
AU - Junming Cao
AU - Wei Li
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.33284
UR - https://arxiv.org/abs/2610.33284
AB - We prove a weak type (1,1) estimate for maximal truncations of noncommutative rough singular integrals whose angular kernels satisfy the classical Llog 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 Calderón--Zygmund decomposition.
ER -