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Sharp rate of average decay of the Fourier transform of a bounded set

L. Brandolini·S. Hofmann·A. Iosevich
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Abstract

We prove that the spherical mean of the Fourier transform of the characteristic function of a bounded convex set (without any additional assumptions) or a bounded set with a C^{3/2} boundary decays at infinity at the same rate as the Fourier transform of the characteristic function of the ball.

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L. Brandolini, S. Hofmann, A. Iosevich. 2003-03-15. Sharp rate of average decay of the Fourier transform of a bounded set. https://arxiv.org/abs/math/0303188

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