On the Fourier transform of the characteristic functions of domains with $C^1$ -smooth boundary

Details On the Fourier transform of the characteristic functions of domains with $C^1$ -smooth boundary On the Fourier transform of the characteristic functions of domains with $C^1$ -smooth boundary

2012-01-02

arxiv.org/abs/1201.0408v2

Mathematics

Classical Analysis and ODEs

added two references; added footnotes on pages 6 and 14

Scientific paper

We consider domains $D\subseteq\mathbb R^n$ with $C^1$ -smooth boundary and
study the following question: when the Fourier transform $\hat{1_D}$ of the
characteristic function $1_D$ belongs to $L^p(\mathbb R^n)$?

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