Weighted wave envelope estimates for the parabola
Jongchon Kim, Hyerim Ko
TL;DR
This paper extends the Córdoba-Fefferman square function estimate for the parabola to a weighted setting, providing new bounds involving multiscale tubes and weight parameters, with applications to Fourier multipliers and Schrödinger solutions.
Contribution
It introduces a weighted wave envelope estimate for the parabola, advancing the understanding of weighted Fourier analysis and PDE solutions.
Findings
Derived weighted square function estimates for the parabola.
Established weighted L^p-estimates for Fourier multipliers.
Applied results to solutions of the free Schrödinger equation.
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.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Advanced Harmonic Analysis Research · Numerical methods in inverse problems