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Transference for Banach Space Representations of Nilpotent Lie Groups. Part 2. Pedersen Multipliers
The Journal of Geometric Analysis ( IF 1.2 ) Pub Date : 2021-06-26 , DOI: 10.1007/s12220-021-00728-8
Ingrid Beltiţă , Daniel Beltiţă , José E. Galé

We characterize twisted convolutions associated with the Pedersen transform for unitary irreducible representations of nilpotent Lie groups. For \(1\le p<\infty \), we also prove the \(L^p\)-boundedness for the Pedersen \(L^p\)-multipliers in the case of unitary irreducible representations that are square-integrable modulo the center of the group under consideration, thus, generalizing an earlier result on Weyl multipliers associated to the pseudo-differential Weyl calculus.



中文翻译:

幂零李群的巴拿赫空间表示的转移。第 2 部分。 Pedersen 乘数

我们描述了与 Pedersen 变换相关的扭曲卷积,用于幂零李群的幺正不可约表示。对于\(1个\文件P <\ infty \) ,我们还证明了\(L ^ P \)有界的彼得森\(L ^ P \) -multipliers在单一不可约表示是平方可积的情况下对所考虑的群的中心取模,从而推广与伪微分 Weyl 演算相关的 Weyl 乘子的早期结果。

更新日期:2021-06-28
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