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arXiv · 2610.29721

Higher rank spectral projector estimates and a Stein--Tomas restriction theorem

Phillip Harris·Jiaqi Hou·Xiaoqi Huang
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Abstract

Let $X$ be a compact locally symmetric space of noncompact type. We prove sharp upper bounds for the $L^2\to L^p$ operator norms of spectral projectors for joint eigenfunctions of the full ring of invariant differential operators on $X$. This improves the corresponding result of Marshall, by removing a logarithmic power loss at the critical exponent. Using the same method, we also prove the endpoint case of Mockenhaupt's $(L^2,L^p)$ Fourier restriction theorem.

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Phillip Harris, Jiaqi Hou, Xiaoqi Huang. 2026-10-21. Higher rank spectral projector estimates and a Stein--Tomas restriction theorem. https://arxiv.org/abs/2610.29721

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