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Weak type (1,1) estimates for noncommutative rough singular integrals
Abstract
We establish the weak type (1,1) endpoint estimate for operator-valued rough singular integrals with kernels satisfying the classical Llog L integrability and cancellation conditions. This extends Seeger's endpoint theorem [{J. Amer. Math. Soc.} \textbf{9} (1996)] to the noncommutative setting. A key ingredient is an off-diagonal analysis that controls interactions between different kernel scales and avoids an additional logarithmic loss.
Related
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BibTeX
@misc{cao2026weak,
title = {{Weak type $(1,1)$ estimates for noncommutative rough singular integrals}},
author = {Junming Cao and Wei Li and Lian Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15633},
eprint = {2610.15633},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15633},
}
RIS
TY - UNPB
TI - Weak type (1,1) estimates for noncommutative rough singular integrals
AU - Junming Cao
AU - Wei Li
AU - Lian Wu
PY - 2026
DA - 2026/10/17
PB - arXiv
DO - 10.48550/arxiv.2610.15633
UR - https://arxiv.org/abs/2610.15633
AB - We establish the weak type (1,1) endpoint estimate for operator-valued rough singular integrals with kernels satisfying the classical Llog L integrability and cancellation conditions. This extends Seeger's endpoint theorem [{J. Amer. Math. Soc.} \textbf{9} (1996)] to the noncommutative setting. A key ingredient is an off-diagonal analysis that controls interactions between different kernel scales and avoids an additional logarithmic loss.
ER -