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Space curve Fourier restriction for orthonormal functions
Abstract
We prove a variant of the L2 Fourier restriction inequality for non-degenerate curves in the setting of orthonormal systems. To achieve this, we develop a Hilbert space approach to studying the L2 theory for Fourier restriction for curves. Our arguments also rely on novel Lp-improving bounds for associated convolution operators, which take averages over neighbourhoods of cones generated by the curve. The Lp-improving bound are established using a variant of the high-low method, in particular using induction-on-scale.
Related
BibTeX
@misc{cuenin2026space,
title = {{Space curve Fourier restriction for orthonormal functions}},
author = {Jean-Claude Cuenin and Jacob Denson and Jonathan Hickman},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.02596},
eprint = {2610.02596},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.02596},
}
RIS
TY - UNPB
TI - Space curve Fourier restriction for orthonormal functions
AU - Jean-Claude Cuenin
AU - Jacob Denson
AU - Jonathan Hickman
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.02596
UR - https://arxiv.org/abs/2610.02596
AB - We prove a variant of the L^2 Fourier restriction inequality for non-degenerate curves in the setting of orthonormal systems. To achieve this, we develop a Hilbert space approach to studying the L^2 theory for Fourier restriction for curves. Our arguments also rely on novel L^p-improving bounds for associated convolution operators, which take averages over neighbourhoods of cones generated by the curve. The L^p-improving bound are established using a variant of the high-low method, in particular using induction-on-scale.
ER -