PreprintCC BY 4.0arXiv
Higher rank spectral projector estimates and a Stein--Tomas restriction theorem
Abstract
Let X be a compact locally symmetric space of noncompact type. We prove sharp upper bounds for the L2→ Lp 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 (L2,Lp) Fourier restriction theorem.
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BibTeX
@misc{harris2026higher,
title = {{Higher rank spectral projector estimates and a Stein--Tomas restriction theorem}},
author = {Phillip Harris and Jiaqi Hou and Xiaoqi Huang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.29721},
eprint = {2610.29721},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.29721},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Higher rank spectral projector estimates and a Stein--Tomas restriction theorem
AU - Phillip Harris
AU - Jiaqi Hou
AU - Xiaoqi Huang
PY - 2026
DA - 2026/10/21
PB - arXiv
DO - 10.48550/arxiv.2610.29721
UR - https://arxiv.org/abs/2610.29721
AB - Let X be a compact locally symmetric space of noncompact type. We prove sharp upper bounds for the L^2→ 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.
ER -