Estimates for singular radon transforms and pseudodifferential operators with singular symbols
Estimates for singular radon transforms and pseudodifferential operators with singular symbols
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DOI：
10.1016/0022-1236(90)90011-9
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发表时间：
1990-03
影响因子：
1.7
通讯作者：
A. Greenleaf;G. Uhlmann
中科院分区：
文献类型：
--
作者：
A. Greenleaf;G. Uhlmann
近年来，人们对将Calderbn-Zygmund奇异积分理论推广到核在子流形上（或沿子流形沿着）的算子有相当大的兴趣。除了extensivt：通过对沿沿着曲线的希尔伯特变换的研究，Lz和Lp估计为：Geller和Stein [GS]，l&iller [Mu I，Mu II]，Greenleaf [G]，Ricci和Stein [RS]证明了幂零李群上的卷积不变算子的卷积核在群单位元和沿着32维子流形上都是奇异的，其中在最后三个参考文献中，子流形在单位元处不一定是光滑的。非平移”不变算子与平滑：？Phollg和Stein [PS I，PS II]曾引入并研究了一类变化的子流形族，但他们假定子流形是光滑的，且在Schwartz核的奇异支集的余正规丛是局部正则变换的图的意义下是非退化的.这种非简并状态被称为“旋转体！曲率。”Uhimann [U]证明了一类带奇异符号的伪微分算子的L '估计，
There has been considerable interest in recent years in extending the theory ol Calderbn-Zygmund singular integrals to operators whose kernels are cont: entrated on (or singular along) submanifolds. Aside from the extensivt: work on Hilbert transforms along curves, Lz and Lp estimates have be: n proven for translation-invariant operators on nilpotent Lie groups jrhose convolution kernels are singular both at the group identity element and along a submanifold of dimension 32 by Geller and Stein [GS], l&iller [Mu I, Mu II], Greenleaf [G], and Ricci and Stein [RS], where in the last three references the submanifold is not necessarily smooth at the identity. Nontranslation” invariant operators associated with a smoothl:? varying family of submanifolds have been introduced and studied by Phollg and Stein [PS I, PS II]; they, however, assume that the submaniYolds are smooth and nondegenerate in the sense that the conormal bundle cf the singular support of the Schwartz kernel is locally the graph of a car onical transformation. This nondegeneracy condition they term “rotatior! aI curvature.” Uhimann [U] proved L’estimates for a class of pseudod fferential operators with singular symbols associated with two