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Weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels

  • Xudong Lai
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Abstract

In this paper, we establish the weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels. To deal with the rough kernels, we develop some orthogonality of the kernels themselves in the pseudo-localization arguments for the good functions and use the microlocal decomposition and TT* arguments for the bad functions.

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Cite

BibTeXRIS
BibTeX
@misc{lai2026weak,
  title = {{Weak type $(1,1)$ boundedness of noncommutative singular integral operators with rough kernels}},
  author = {Xudong Lai},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.38671},
  eprint = {2609.38671},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.38671},
}
RIS
TY  - UNPB
TI  - Weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels
AU  - Xudong Lai
PY  - 2026
DA  - 2026/09/29
PB  - arXiv
DO  - 10.48550/arxiv.2609.38671
UR  - https://arxiv.org/abs/2609.38671
AB  - In this paper, we establish the weak type (1,1) boundedness of noncommutative singular integral operators with rough kernels. To deal with the rough kernels, we develop some orthogonality of the kernels themselves in the pseudo-localization arguments for the good functions and use the microlocal decomposition and TT^* arguments for the bad functions.
ER  -