发表机构
Université d’Evry Val d’Essonne; Universidad de las Américas（埃夫里-瓦勒德埃松大学; 美洲大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究分层李群上带权粗糙奇异积分算子的逐点估计，推导新带权泛函不等式，应用于得到Heisenberg群上定常Navier-Stokes方程粗糙形式的唯一性结果。
AI 中文摘要
本文在分层李群的框架下，给出了带权粗糙奇异积分算子的新逐点估计。该算子记为$T_{\Omega, \varpi}$，基于核函数$\Omega$和权函数$\varpi$，其中核函数满足关于权函数$\varpi$的自然大小条件和消去性质，且不对这些对象施加任何正则性假设。将该带权粗糙奇异积分算子作用于函数$f$时，通过结合$f$梯度的带权极大函数信息与带权Morrey空间来估计。我们还从该逐点估计中推导出一些新的带权泛函不等式，并作为应用得到了Heisenberg群上定常Navier-Stokes方程的粗糙形式的唯一性结果。
英文摘要
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, $T_{Ω, \varpi}$, is based on a kernel $Ω$ 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.
Comments19 pages
