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On a pointwise estimate for a weighted rough singular integral operator in stratified Lie groups and applications

  • Diego Chamorro
  • Oscar Jarrín
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Abstract

In this article, we present a new pointwise estimate for a weighted rough singular integral operator in the setting of stratified Lie groups. This operator, TΩ, ϖ, is based on a kernel Ω and a weight ϖ, where the kernel satisfies a natural size condition and a cancellation property with respect to the weight ϖ. Moreover, we do not assume any kind of regularity on these objects. This weighted rough singular integral operator, applied to a function f, is estimated through a combination of information involving a weighted maximal function of the gradient of f and a weighted Morrey space. We also deduce from this pointwise estimate some new weighted functional inequalities and, as an application, we obtain a uniqueness result for a rough version of the stationary Navier-Stokes equation over the Heisenberg group.

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Cite

BibTeXRIS
BibTeX
@misc{chamorro2026pointwise,
  title = {{On a pointwise estimate for a weighted rough singular integral operator in stratified Lie groups and applications}},
  author = {Diego Chamorro and Oscar Jarrín},
  howpublished = {arXiv},
  year = {2026},
  month = aug,
  doi = {10.48550/arxiv.2608.30970},
  eprint = {2608.30970},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.30970},
}
RIS
TY  - UNPB
TI  - On a pointwise estimate for a weighted rough singular integral operator in stratified Lie groups and applications
AU  - Diego Chamorro
AU  - Oscar Jarrín
PY  - 2026
DA  - 2026/08/31
PB  - arXiv
DO  - 10.48550/arxiv.2608.30970
UR  - https://arxiv.org/abs/2608.30970
AB  - In this article, we present a new pointwise estimate for a weighted rough singular integral operator in the setting of stratified Lie groups. This operator, T_Ω, ϖ, is based on a kernel Ω and a weight ϖ, where the kernel satisfies a natural size condition and a cancellation property with respect to the weight ϖ. Moreover, we do not assume any kind of regularity on these objects. This weighted rough singular integral operator, applied to a function f, is estimated through a combination of information involving a weighted maximal function of the gradient of f and a weighted Morrey space. We also deduce from this pointwise estimate some new weighted functional inequalities and, as an application, we obtain a uniqueness result for a rough version of the stationary Navier-Stokes equation over the Heisenberg group.
ER  -