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arXiv · 1804.03605

Extremizability of Fourier restriction to the paraboloid

Betsy Stovall
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Abstract

In this article, we prove that all global, nonendpoint Fourier restriction inequalities for the paraboloid in $\mathbb R^{1+d}$ have extremizers and that $L^p$-normalized extremizing sequences are precompact modulo symmetries. This result had previously been established for the case $q=2$. In the range where the boundedness of the restriction operator is still an open question, our result is conditional on improvements toward the restriction conjecture.

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Betsy Stovall. 2018-04-10. Extremizability of Fourier restriction to the paraboloid. https://doi.org/10.1016/j.aim.2019.106898

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