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Restriction of Fourier transforms to curves: An endpoint estimate with affine arclength measure

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arxiv 1109.1300 v2 pith:PF3AEGN5 submitted 2011-09-06 math.CA math.FA

Restriction of Fourier transforms to curves: An endpoint estimate with affine arclength measure

classification math.CA math.FA
keywords affinearclengthcurvecurvesendpointestimatefouriermeasure
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Consider the Fourier restriction operator associated to a curve in $R^d$, $d\ge 3$. We prove for various classes of curves the endpoint restricted strong type estimate with respect to affine arclength measure on the curve. An essential ingredient is an interpolation result for multilinear operators with symmetries acting on sequences of vector-valued functions.

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