Weighted wave envelope estimates for the parabola
Classical Analysis and ODEs
2025-12-23 v2 Analysis of PDEs
Abstract
In this paper, we extend the C\'ordoba-Fefferman square function estimate for the parabola to a weighted setting. Our weighted square function estimate is derived from a weighted wave envelope estimate for the parabola. The bounds are formulated in terms of families of multiscale tubes together with weight parameters that quantify the distribution of the weight. As an application, we obtain some weighted L^p-estimates for a class of Fourier multiplier operators and for solutions to free Schr\"odinger equation.
Keywords
Cite
@article{arxiv.2511.04503,
title = {Weighted wave envelope estimates for the parabola},
author = {Jongchon Kim and Hyerim Ko},
journal= {arXiv preprint arXiv:2511.04503},
year = {2025}
}
Comments
Incorporated additional references, replaced a polylogarithmic factor by a sub-polynomial factor in main results, and revised Section 4.2 for clarity