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- W2749295708 abstract "The $L^2 to L^p$ adjoint Fourier restriction inequality on the $d$-dimensional hyperboloid $mathbb{H}^d subset mathbb{R}^{d+1}$ holds provided $6 leq p < infty$, if $d=1$, and $2(d+2)/d leq pleq 2(d+1)/(d-1)$, if $dgeq2$. Quilodr'{a}n recently found the values of the optimal constants in the endpoint cases $(d,p)in{(2,4),(2,6),(3,4)}$ and showed that the inequality does not have extremizers in these cases. In this paper we answer two questions posed by Quilodr'{a}n, namely: (i) we find the explicit value of the optimal constant in the endpoint case $(d,p) = (1,6)$ (the remaining endpoint for which $p$ is an even integer) and show that there are no extremizers in this case; and (ii) we establish the existence of extremizers in all non-endpoint cases in dimensions $d in {1,2}$. This completes the qualitative description of this problem in low dimensions." @default.
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- W2749295708 date "2017-08-12" @default.
- W2749295708 modified "2023-09-27" @default.
- W2749295708 title "Extremizers for Fourier restriction on hyperboloids" @default.
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