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arXiv · 2610.02596

Space curve Fourier restriction for orthonormal functions

Jean-Claude Cuenin·Jacob Denson·Jonathan Hickman
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Abstract

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.

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Jean-Claude Cuenin, Jacob Denson, Jonathan Hickman. 2026-10-01. Space curve Fourier restriction for orthonormal functions. https://arxiv.org/abs/2610.02596

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