Phase-Space Analysis and Pseudodifferential Calculus on the Heisenberg Group
Phase-Space Analysis and Pseudodifferential Calculus on the Heisenberg Group
复制标题
海森堡群的相空间分析与伪微分
DOI：
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发表时间：
2009
期刊：
影响因子：
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通讯作者：
I. Gallagher
中科院分区：
文献类型：
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作者：
H. Bahouri;C. Fermanian;I. Gallagher
定义了一类海森堡群上的伪微分算子。应该如此，此类是包含微分运算符类的代数。此外，这些伪微分算子连续作用于Sobolev空间，并且导数的损失可以通过算子的阶数来控制。尽管过去有大量工作致力于变系数算子代数的构造和研究，包括一些关于海森堡群的非常有趣的工作，但我们的方法是不同的，特别是采用了轻微局域方向并完成了~\cite{bgx}和~\cite{bg}中发展的Littlewood-Paley理论，对 海森堡小组。
A class of pseudodifferential operators on the Heisenberg group is defined. As it should be, this class is an algebra containing the class of differential operators. Furthermore, those pseudodifferential operators act continuously on Sobolev spaces and the loss of derivatives may be controled by the order of the operator. Although a large number of works have been devoted in the past to the construction and the study of algebras of variable-coefficient operators, including some very interesting works on the Heisenberg group, our approach is different, and in particular puts into light microlocal directions and completes, with the Littlewood-Paley theory developed in~\cite{bgx} and~\cite{bg}, a microlocal analysis of the Heisenberg group.