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On the Fourier transform of the characteristic functions of domains with C1C^1 -smooth boundary

Abstract

We consider domains DRnD\subseteq\mathbb R^n with C1C^1 -smooth boundary and study the following question: when the Fourier transform 1D^\hat{1_D} of the characteristic function 1D1_D belongs to Lp(Rn)L^p(\mathbb R^n)?Comment: added two references; added footnotes on pages 6 and 1

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