Geodesic
On the Fourier Transform of the Characteristic Functions of Domains with $C^1$ Boundary
Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 1, pp. 33-46.

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We consider domains $D\subseteq\mathbb R^n$ with $C^1$ boundary and study the following question: For what domains $D$ does the Fourier transform $\widehat{1_D}$ of the characteristic function $1_D$ belong to $L^p(\mathbb R^n)$?
Keywords: harmonic analysis, domain with smooth boundary, Fourier transform of a characteristic function. 
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V. V. Lebedev. On the Fourier Transform of the Characteristic Functions of Domains with $C^1$ Boundary. Funkcionalʹnyj analiz i ego priloženiâ, Tome 47 (2013) no. 1, pp. 33-46. http://geodesic.mathdoc.fr/item/FAA_2013_47_1_a3/

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