论文标题
重新审视分级谎言组的奇异整体操作员
Oscillating singular integral operators on graded Lie groups revisited
论文作者
论文摘要
在这项工作中，我们将由于fefferman和Stein引起的欧克里德裔振荡理论\ cite {fefferman1970，feffermanstein1972}延伸到任意分级的谎言组。我们的方法揭示了分级谎言组的几何测量理论与与洛克兰运营商相关的傅立叶分析之间的强烈兼容性。我们的标准是根据操作员内核及其组傅立叶变换的振荡Fefferman条件提出的。这项工作的新事物之一是，我们使用岩石运营商的无限表示来测量核的傅立叶变换的衰变。
In this work, we extend the Euclidean theory of oscillating singular integrals due to Fefferman and Stein in \cite{Fefferman1970,FeffermanStein1972} to arbitrary graded Lie groups. Our approach reveals the strong compatibility between the geometric measure theory of a graded Lie group and the Fourier analysis associated with Rockland operators. Our criteria are presented in terms of the oscillating Fefferman condition of the kernel of the operator and its group Fourier transform. One of the novelties of this work is that we use the infinitesimal representation of a Rockland operator to measure the decay of the Fourier transform of the kernel.
