PreprintCC BY 4.0arXiv
A Mizohata--Takeuchi-type estimate for the hyperbolic paraboloid
Abstract
We prove Mizohata--Takeuchi-type estimates for the Fourier extension operator associated with the truncated hyperbolic paraboloid in R3. Our main result controls the weighted L2 norm of the extension operator by the L2 mass of the weight over a multiscale family of parallelepipeds arising from ℓ2 decoupling for the hyperbolic paraboloid. We deduce this result from a weighted L2 estimate for functions whose Fourier transforms are supported in a small neighborhood of the hyperbolic paraboloid, which we establish using a bilinear refined decoupling estimate.
Related
- Global Mizohata-Takeuchi for Indicator Weights of Bounded Complexity in ℝ2
- Resolvent estimate for asymptotically hyperbolic surfaces without evenness assumption
- Dolgopyat estimate for partially hyperbolic systems: limit theorems and exponential mixing
- A Gage-type estimate for the p-fundamental tone and applications to submanifolds
- A Cheng-Yau type estimate for positive biharmonic functions
BibTeX
@misc{kim2026mizohatatakeuchitype,
title = {{A Mizohata--Takeuchi-type estimate for the hyperbolic paraboloid}},
author = {Jongchon Kim and Liang Wang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.07909},
eprint = {2610.07909},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.07909},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Mizohata--Takeuchi-type estimate for the hyperbolic paraboloid
AU - Jongchon Kim
AU - Liang Wang
PY - 2026
DA - 2026/10/16
PB - arXiv
DO - 10.48550/arxiv.2610.07909
UR - https://arxiv.org/abs/2610.07909
AB - We prove Mizohata--Takeuchi-type estimates for the Fourier extension operator associated with the truncated hyperbolic paraboloid in R^3. Our main result controls the weighted L^2 norm of the extension operator by the L^2 mass of the weight over a multiscale family of parallelepipeds arising from ℓ^2 decoupling for the hyperbolic paraboloid. We deduce this result from a weighted L^2 estimate for functions whose Fourier transforms are supported in a small neighborhood of the hyperbolic paraboloid, which we establish using a bilinear refined decoupling estimate.
ER -