论文标题
Hörmander-Mikhlin定理的高级简单谎言组
A Hörmander-Mikhlin theorem for high rank simple Lie groups
论文作者
论文摘要
我们建立了$ l_p $ - 结合的规律性条件，该组在von Neumann代数上，具有更高等级的简单谎言组。这提供了自然的Hörmander-Mikhlin标准，该标准就符号的谎言衍生物和伴随代表给出的度量标准提供了。与Lafforgue/de la Salle的刚性定理一致，我们的病情在无穷大处施加了某些符号的衰减。它以$ \ sl $的价格完善了Parcet，Ricard和de la Salle的最新结果。我们的方法部分是基于任意谎言群体的尖锐局部Hörmander-Mikhlin定理，而这反过来又是根据作者对单数非Nontoeplitz Schur乘数的最新估计。我们将后者推广到任意局部紧凑的组，并通过Junge，MEI和Parcet在组代数中使用基于Cocycle的方法。还讨论了一些相关的开放问题。
We establish regularity conditions for $L_p$-boundedness of Fourier multipliers on the group von Neumann algebras of higher rank simple Lie groups. This provides a natural Hörmander-Mikhlin criterion in terms of Lie derivatives of the symbol and a metric given by the adjoint representation. In line with Lafforgue/de la Salle's rigidity theorem, our condition imposes certain decay of the symbol at infinity. It refines and vastly generalizes a recent result by Parcet, Ricard and de la Salle for $\SL$. Our approach is partly based on a sharp local Hörmander-Mikhlin theorem for arbitrary Lie groups, which follows in turn from recent estimates by the authors on singular nonToeplitz Schur multipliers. We generalize the latter to arbitrary locally compact groups and refine the cocycle-based approach to Fourier multipliers in group algebras by Junge, Mei and Parcet. A few related open problems are also discussed.
