An invitation to harmonic analysis associated with semigroups of operators
An invitation to harmonic analysis associated with semigroups of operators
复制标题
DOI：
10.1090/conm/612/12227
复制
发表时间：
2013-04
期刊：
影响因子：
--
通讯作者：
M. Junge;T. Mei;Javier Parcet
中科院分区：
文献类型：
--
作者：
M. Junge;T. Mei;Javier Parcet
本文介绍了我们最近在算子半群的调和分析方面的工作，试图为von Neumann代数找到一个非交换的Calder\'on-Zygmund理论。经典的CZ理论传统上是在满足附加正则性的度量测度空间上发展起来的。在缺乏这样的度量-或与非常少的信息度量-马尔可夫半群的运营商似乎是正确的替代品的经典度量/几何工具在调和分析。我们的方法是特别有用的非交换设置，但它也是有效的经典/交换框架。
This article is an introduction to our recent work in harmonic analysis associated with semigroups of operators, in the effort of finding a noncommutative Calder\'on-Zygmund theory for von Neumann algebras. The classical CZ theory has been traditionally developed on metric measure spaces satisfying additional regularity properties. In the lack of such metrics -or with very little information on the metric- Markov semigroups of operators appear to be the right substitutes of classical metric/geometric tools in harmonic analysis. Our approach is particularly useful in the noncommutative setting but it is also valid in classical/commutative frameworks.