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Sparse bounds for rough non-translation-invariant Calderón-Zygmund operators

  • Yanping Chen
  • Teng Wang
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Abstract

In this paper, we establish sparse bounds for singular integral operators with rough non-translation-invariant Calderón-Zygmund kernels. Our approach verifies the localized hypothesis in the sparse domination framework introduced by Conde-Alonso, Di Plinio et al. The proof refines Seeger's microlocal decomposition using a Littlewood-Paley analysis adapted to the non-translation-invariant setting. As applications, we obtain quantitative weighted estimates for Calderón-type commutators and other singular integrals with rough kernels.

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Cite

BibTeXRIS
BibTeX
@misc{chen2026sparse,
  title = {{Sparse bounds for rough non-translation-invariant Calderón-Zygmund operators}},
  author = {Yanping Chen and Teng Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.19468},
  eprint = {2610.19468},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.19468},
}
RIS
TY  - UNPB
TI  - Sparse bounds for rough non-translation-invariant Calderón-Zygmund operators
AU  - Yanping Chen
AU  - Teng Wang
PY  - 2026
DA  - 2026/10/14
PB  - arXiv
DO  - 10.48550/arxiv.2610.19468
UR  - https://arxiv.org/abs/2610.19468
AB  - In this paper, we establish sparse bounds for singular integral operators with rough non-translation-invariant Calderón-Zygmund kernels. Our approach verifies the localized hypothesis in the sparse domination framework introduced by Conde-Alonso, Di Plinio et al. The proof refines Seeger's microlocal decomposition using a Littlewood-Paley analysis adapted to the non-translation-invariant setting. As applications, we obtain quantitative weighted estimates for Calderón-type commutators and other singular integrals with rough kernels.
ER  -