Year: 2024
Type: preprint
Abstract: We show sharp square function estimates for curves in the plane whose curvature degenerates at a point and estimates sharp up to endpoints for cones over these curves. To this end, for curves of finite type we extend the classical Córdoba--Fefferman biorthogonality. For cones over degenerate curves, we analyze wave envelope estimates proved via High-Low-decomposition. The arguments are subsequently extended to the cone over the complex parabola.
Source: arXiv (Cornell University)
Author: Schippa, Robert
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: National Science Foundation
Award: Nonlinear Dispersive Waves
OpenAlex ID: W4402427638