Uniform estimates for the local restriction of the Fourier transform to curves

Dendrinos, Spyridon; Müller, Detlef

doi:10.1090/S0002-9947-2012-05769-2

Uniform estimates for the local restriction of the Fourier transform to curves
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by Spyridon Dendrinos and Detlef Müller PDF

Trans. Amer. Math. Soc. 365 (2013), 3477-3492 Request permission

Abstract:

We prove sharp estimates, with respect to the affine arclength measure, for the restriction of the Fourier transform to a class of curves in $\mathbb {R}^d$ that includes curves of finite type. This measure possesses certain invariance and mitigation properties which are important in establishing uniform results.

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