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arXiv · 2111.06874

Uniform Fourier restriction for convex curves

Marco Fraccaroli
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Abstract

We extend the estimates for maximal Fourier restriction operators proved by M\"{u}ller, Ricci, and Wright in \cite{MR3960255} and Ramos in \cite{MR4055940} to the case of arbitrary convex curves in the plane, with constants uniform in the curve. The improvement over M\"{u}ller, Ricci, and Wright and Ramos is given by the removal of the $\mathcal{C}^2$ regularity condition on the curve. This requires the choice of an appropriate measure for each curve, that is suggested by an affine invariant construction of Oberlin in \cite{MR1960918}. As corollaries, we obtain a uniform Fourier restriction theorem for arbitrary convex curves, and a result on the Lebesgue points of the Fourier transform on the curve.

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Marco Fraccaroli. 2021-11-12. Uniform Fourier restriction for convex curves. https://doi.org/10.1007/s10231-023-01417-9

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