A noncommutative weak L₁-estimate for rough singular integrals

@misc{hong2026noncommutative,
  title = {{A noncommutative weak $L_1$-estimate for rough singular integrals}},
  author = {Guixiang Hong and Liang Wang and Xumin Wang and Bang Xu},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.25339},
  eprint = {2610.25339},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.25339},
}

TY  - UNPB
TI  - A noncommutative weak L_1-estimate for rough singular integrals
AU  - Guixiang Hong
AU  - Liang Wang
AU  - Xumin Wang
AU  - Bang Xu
PY  - 2026
DA  - 2026/10/18
PB  - arXiv
DO  - 10.48550/arxiv.2610.25339
UR  - https://arxiv.org/abs/2610.25339
AB  - 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 Llog 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.
ER  -