抛物面上的伴随Fourier限制不等式的Gaussians Rare证明
Gaussians Rarely Extremize Adjoint Fourier Restriction Inequalities For Paraboloids
摘要：
Foschi和Hundertmark，Zharnitsky分别证明了抛物面上L^2函数的伴随傅里叶限制不等式在两种最低维情形下的高斯极值化。本文证明了高斯型是L^p到L^q伴随Fourier限制不等式的临界点当且仅当p=2.此外，高斯型是（1，无穷大）^2中所有容许对（r，q）的L^2到L^r_t L^q_x哈茨不等式的临界点。
英文摘要：
It was proved independently by Foschi and Hundertmark, Zharnitsky that Gaussians extremize the adjoint Fourier restriction inequality for L^2 functions on the paraboloid in the two lowest-dimesional cases. Here we prove that Gaussians are critical points for the L^p to L^q adjoint Fourier restriction inequalities if and only if p=2. Also, Gaussians are critial points for the L^2 to L^r_t L^q_x Strichartz inequalities for all admissible pairs (r,q) in (1,infinity)^2.
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