Remarks on space curve L² Fourier restriction

@misc{cuenin2026remarks,
  title = {{Remarks on space curve $L^2$ Fourier restriction}},
  author = {Jean-Claude Cuenin and Jacob Denson and Jonathan Hickman},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.27968},
  eprint = {2610.27968},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.27968},
}

TY  - UNPB
TI  - Remarks on space curve L^2 Fourier restriction
AU  - Jean-Claude Cuenin
AU  - Jacob Denson
AU  - Jonathan Hickman
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.27968
UR  - https://arxiv.org/abs/2610.27968
AB  - 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.
ER  -