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arXiv · 2608.30970

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, $T_{\Omega, \varpi}$, is based on a kernel $\Omega$ and a weight $\varpi$, where the kernel satisfies a natural size condition and a cancellation property with respect to the weight $\varpi$. 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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Diego Chamorro, Oscar Jarrín. 2026-08-31. On a pointwise estimate for a weighted rough singular integral operator in stratified Lie groups and applications. https://arxiv.org/abs/2608.30970

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