PreprintCC0arXiv
A weighted restriction estimate in ℝ2
Abstract
We establish a weighted restriction estimate in ℝ2. Our proof combines new two-ends Furstenberg estimates with refined decoupling.As an application, our result yields decay estimates for the circular Lp-means of the Fourier transforms of fractal measures in ℝ2.
Related
- Transference theory for the trilinear restriction estimate and an application to the quadratic NLS in 3D
- The (n−2)-linear restriction estimate in ℝn
- The (n−1)-linear restriction estimate in ℝn with degenerate curvature
- Endpoint weighted Fourier estimate with vanishing spherical trace
- Lp-weighted cone restriction estimates
BibTeX
@misc{cao2026weighted,
title = {{A weighted restriction estimate in $\mathbb R^2$}},
author = {Zhenbin Cao and Feilong Guo and Junfeng Li and Xiangyu Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2609.12587},
eprint = {2609.12587},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.12587},
note = {CC0},
}
RIS
TY - UNPB
TI - A weighted restriction estimate in ℝ^2
AU - Zhenbin Cao
AU - Feilong Guo
AU - Junfeng Li
AU - Xiangyu Wang
PY - 2026
DA - 2026/10/03
PB - arXiv
DO - 10.48550/arxiv.2609.12587
UR - https://arxiv.org/abs/2609.12587
AB - We establish a weighted restriction estimate in ℝ^2. Our proof combines new two-ends Furstenberg estimates with refined decoupling.As an application, our result yields decay estimates for the circular L^p-means of the Fourier transforms of fractal measures in ℝ^2.
ER -