振荡奇异积分在多项式增长的李群上的有界性
Boundedness of oscillating singular integrals on Lie groups of polynomial growth
摘要：
研究了多项式增长的李群上振荡奇异积分的有界性，推广了February man和Stein关于振荡卷积算子有界性的经典振荡条件.核准则是根据一个固定的子黎曼结构的诱导组的子拉普拉斯算子相关联的一个Hörmander系统的向量场。在分组的情况下，核标准的傅里叶分析与任意Rockland运营商。
英文摘要：
We investigate the boundedness of oscillating singular integrals on Lie groups of polynomial growth in order to extend the classical oscillating conditions due to Fefferman and Stein for the boundedness of oscillating convolution operators. Kernel criteria are presented in terms of a fixed sub-Riemannian structure on the group induced by a sub-Laplacian associated to a Hörmander system of vector fields. In the case where the group is graded, kernel criteria are presented in terms of the Fourier analysis associated to an arbitrary Rockland operator.
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