欧氏二维环上谱投影的 L2 到 Lp 边界

Pub Date : 2024-03-15 DOI:10.1017/s0013091524000099

Ciprian Demeter, Pierre Germain

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引用次数: 0

摘要

我们考虑了与二维环上欧氏拉普拉奇相关的谱投影，即谱窗很窄的情况。我们推导了其 L2 到 Lp 算子规范的边界，扩展了索格的经典结果；引入了关于投影器卷积核的新问题。所采用的方法包括 $\ell^2$ 去耦、小上限去耦和指数和的估计。

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L2 to Lp bounds for spectral projectors on the Euclidean two-dimensional torus

We consider spectral projectors associated to the Euclidean Laplacian on the two-dimensional torus, in the case where the spectral window is narrow. Bounds for their L2 to Lp operator norm are derived, extending the classical result of Sogge; a new question on the convolution kernel of the projector is introduced. The methods employed include

$\ell^2$

decoupling, small cap decoupling and estimates of exponential sums.

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