Year: 2026
Type: preprint
Abstract: 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 $\ell^2$ 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.
Source: arXiv (Cornell University)
Authors: Kim, Jongchon, Wang, Liang
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: City University of Hong Kong
OpenAlex ID: W7220971735