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arXiv · 2209.06981

Sharp Fourier extension on fractional surfaces

Boning Di·Dunyan Yan
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Abstract

For $\alpha\geq 2$, we investigate a class of Fourier extension operators on fractional surfaces $(\xi,|\xi|^\alpha)$. For the corresponding $\alpha$-Strichartz inequalities, by applying the missing mass method and bilinear restriction theory, we characterize the precompactness of extremal sequences. Our result is valid in any dimension. In particular for dimension two, our result implies the existence of extremals for $\alpha \in [2,\alpha_0)$ with some $\alpha_0>5$.

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Boning Di, Dunyan Yan. 2022-09-15. Sharp Fourier extension on fractional surfaces. https://doi.org/10.1007/s00041-024-10099-7

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