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arXiv · 1809.05698

Extremizers for adjoint Fourier restriction on hyperboloids: the higher dimensional case

Emanuel Carneiro·Diogo Oliveira e Silva·Mateus Sousa·Betsy Stovall
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Abstract

We prove that in dimensions $d \geq 3$, the non-endpoint, Lorentz-invariant $L^2 \to L^p$ adjoint Fourier restriction inequality on the $d$-dimensional hyperboloid $\mathbb{H}^d \subseteq \mathbb{R}^{d+1}$ possesses maximizers. The analogous result had been previously established in dimensions $d=1,2$ using the convolution structure of the inequality at the lower endpoint (an even integer); we obtain the generalization by using tools from bilinear restriction theory.

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Emanuel Carneiro, Diogo Oliveira e Silva, Mateus Sousa, Betsy Stovall. 2018-09-15. Extremizers for adjoint Fourier restriction on hyperboloids: the higher dimensional case. https://doi.org/10.1512/iumj.2021.70.8323

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