分次李群上伪微分算子的$L^p$ -界
$L^p$-bounds for pseudo-differential operators on graded Lie groups
摘要：
本文得到了任意分次李群上伪微分算子的$L^p$ -估计。这些结果是在分次李群上的整体符号演算的背景下，通过对每个分次李群的傅里叶分析得到的，它扩展了Hörmander在$\mathbb{R}^n$上的一般分析.主要结果将经典的关于$\mathbb{R}^n$上Hörmander类的伪微分算子的$L^p$ -有界性的Festerman尖锐定理推广到一般分次李群，并增加了边界$ρ=δ$的情形.
英文摘要：
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 $ρ=δ$ case.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
