Schatten Classes and Commutators of Riesz Transform on Heisenberg Group and Applications
Schatten Classes and Commutators of Riesz Transform on Heisenberg Group and Applications
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DOI：
10.1007/s00041-023-09995-1
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发表时间：
2021-07
影响因子：
1.2
通讯作者：
Zhijie Fan;Michael Lacey;Ji Li
中科院分区：
文献类型：
--
作者：
Zhijie Fan;Michael Lacey;Ji Li
本文研究了Heisenberg群上的Riesz变换分解子。这些符号的Schatten范数的特征在于符号的Besov范数。这推广了Peller，Janson-Wolff和Rochberg-Semmes的经典欧几里德结果。证明中的方法绕过了傅立叶分析的使用，使我们不仅能够解决Riesz变换，而且还可以解决Cauchy-SzegIgn投影和二阶Riesz变换。
We study commutators with the Riesz transforms on the Heisenberg group. The Schatten norm of these commutators is characterized in terms of Besov norms of the symbol. This generalizes the classical Euclidean results of Peller, Janson–Wolff and Rochberg–Semmes. The method in proof bypasses the use of Fourier analysis, allowing us to address not just the Riesz transforms, but also the Cauchy–Szegő projection and second order Riesz transforms onamong other settings.