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

Vladimir Lebedev

doi:10.1007/s10688-013-0004-1

paper

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

arXiv:1201.0408 · doi:10.1007/s10688-013-0004-1

Abstract

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

added two references; added footnotes on pages 6 and 14

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

Abstract

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