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arXiv · 2610.27968

Remarks on space curve $L^2$ Fourier restriction

Jean-Claude Cuenin·Jacob Denson·Jonathan Hickman
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Abstract

We re-examine and consider variants of the Fourier restriction theorem for space curves. In particular, we introduce a Stein--Tomas-type argument which recovers the sharp $L^2$ restriction theorem from classical oscillatory integral estimates, in the spirit of Arkhipov--Chubarikov--Karatsuba. In addition, we consider certain square function estimates which can be thought of as partial progress towards a space curve variant of the orthonormal Fourier restriction theorem of Frank--Sabin. These estimates are obtained by reducing the problem to a Kakeya-type maximal inequality, which we analyse using a formulation of the Bourgain--Guth broad/narrow method.

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Jean-Claude Cuenin, Jacob Denson, Jonathan Hickman. 2026-10-20. Remarks on space curve $L^2$ Fourier restriction. https://arxiv.org/abs/2610.27968

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