On the Fourier transform of the characteristic functions of domains with   $C^1$ -smooth boundary
  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 $L^p(\mathbb R^n)$? 
Vladimir Lebedev
math.CA