Fourier transform and regularity of characteristic functions

Hyerim Ko; Sanghyuk Lee

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arXiv · 1508.04218

Fourier transform and regularity of characteristic functions

Hyerim Ko·Sanghyuk Lee

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Abstract

Let $E$ be a bounded domain in $\mathbb R^d$. We study regularity property of $\chi_E$ and integrability of $\widehat {\chi_E }$ when its boundary $\partial E$ 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.

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Hyerim Ko, Sanghyuk Lee. 2015-08-18. Fourier transform and regularity of characteristic functions. https://arxiv.org/abs/1508.04218

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