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The Fourier restriction problem for biradial functions
Abstract
We determine the exact strong-type Fourier restriction range for the unit sphere 𝕊d−1 on the class of O(d−k)× O(k)-invariant functions, for every d≥4 and 2≤ k≤ d−2. This includes the critical estimates beyond the biradial Stein--Tomas endpoint left open by Mandel and Oliveira e Silva. The proof combines a weighted L2 estimate for extension from a circular arc with the full two-dimensional restriction theorem. An appendix gives a direct proof of the classically conjectured range for axially symmetric functions on the whole sphere.
Related
BibTeX
@misc{kinoshita2026fourier,
title = {{The Fourier restriction problem for biradial functions}},
author = {Shinya Kinoshita and Juyoung Lee and Diogo Oliveira e Silva and Shobu Shiraki},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.27967},
eprint = {2610.27967},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.27967},
}
RIS
TY - UNPB
TI - The Fourier restriction problem for biradial functions
AU - Shinya Kinoshita
AU - Juyoung Lee
AU - Diogo Oliveira e Silva
AU - Shobu Shiraki
PY - 2026
DA - 2026/10/20
PB - arXiv
DO - 10.48550/arxiv.2610.27967
UR - https://arxiv.org/abs/2610.27967
AB - We determine the exact strong-type Fourier restriction range for the unit sphere 𝕊^d−1 on the class of O(d−k)× O(k)-invariant functions, for every d≥4 and 2≤ k≤ d−2. This includes the critical estimates beyond the biradial Stein--Tomas endpoint left open by Mandel and Oliveira e Silva. The proof combines a weighted L^2 estimate for extension from a circular arc with the full two-dimensional restriction theorem. An appendix gives a direct proof of the classically conjectured range for axially symmetric functions on the whole sphere.
ER -