Fourier transform and regularity of characteristic functions

2015/08/18 by Hyerim Ko, Sanghyuk Lee, Ko, Hyerim +1
Computer Science · Mathematics · #Advanced Harmonic Analysis Research #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1508.04218

openalex publication_date 2015/08/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let E be a bounded domain in \mathbb R^d. We study regularity property of χ_E and integrability of \widehat χ_E when its boundary ∂ E satisfies some conditions. At the critical case these properties are generally known to fail. By making use of Lorentz and Lorentz-Sobolev spaces we obtain the endpoint cases of the previous known results. Our results are based on a refined version of Littlewood-Paley inequality, which makes it possible to exploit cancellation effectively.

Citations

• Fractal Geometry: Mathematical Foundations and Applications.

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