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Extremizers for Fourier restriction inequalities: Convex arcs

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Abstract

We establish the existence of extremizers for a Fourier restriction inequality on planar convex arcs without points with collinear tangents whose curvature satisfies a natural assumption. More generally, we prove that any extremizing sequence of nonnegative functions has a subsequence which converges to an extremizer.

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Authors and Affiliations

  1. Department of Mathematics, University of California, Berkeley, CA, 94720-3840, USA

    Diogo Oliveira e Silva

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  1. Diogo Oliveira e Silva
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Correspondence to Diogo Oliveira e Silva.

Additional information

The author was partially supported by the Fundação para a Ciência e a Tecnologia (FCT/Portugal grant SFRH/BD/28041/2006) and the National Science Foundation under agreement DMS-0901569.

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Oliveira e Silva, D. Extremizers for Fourier restriction inequalities: Convex arcs. JAMA 124, 337–385 (2014). https://doi.org/10.1007/s11854-014-0035-4

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  • DOI: https://doi.org/10.1007/s11854-014-0035-4

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