In this work we obtain sharp \(L^p\)-estimates for pseudo-differential operators on arbitrary graded Lie groups. The results are presented within the setting of the global symbolic calculus on graded Lie groups by using the Fourier analysis associated to every graded Lie group which extends the usual one due to Hörmander on \({\mathbb {R}}^n\). The main result extends the classical Fefferman’s sharp theorem on the \(L^p\)-boundedness of pseudo-differential operators for Hörmander classes on \({\mathbb {R}}^n\) to general graded Lie groups, also adding the borderline \(\rho =\delta \) case.

在这项工作中，我们获得了任意渐变李群上伪微分算子的锐利\（L ^ p \）估计。通过使用与每个分级Lie组相关的傅立叶分析，将结果呈现在分级Lie组的全局符号演算的设置中，该傅立叶分析扩展了由于\（{{mathbb {R}} ^ n \）上的Hörmander所引起的通常的傅立叶分析。主要结果将经典Fefferman的关于（\\ {{\ mathbb {R}} ^ n \）上Hörmander类的伪微分算子\（L ^ p \）有界的尖锐定理扩展到一般分级的Lie群，边界\（\ rho = \ delta \）情况。