On the Fourier transform of the characteristic functions of domains with C¹ -smooth boundary
classification
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boundarycharacteristicdomainsfouriermathbbsmoothtransformbelongs
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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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