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

Abstract

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

arXiv commentadded two references; added footnotes on pages 6 and 14

References in corpus (1)

• Estimates in Beurling--Helson type theorems. Multidimensional case

Cited by in corpus (2)

• Recovering a Potential from Cauchy Data via Complex Geometrical Optics Solutions
• Fourier transform and regularity of characteristic functions