Year: 2026
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Harris, Phillip, Hou, Jiaqi, Huang, Xiaoqi
Institutions: University of Bonn, Louisiana State University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7223239792