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arXiv · 2112.13130

Extremizers for Adjoint Restriction to a Pair of Reflected Paraboloids

James Tautges
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Abstract

We consider the adjoint restriction inequality associated to the hypersurface $\{(τ, ξ) : τ= \pm|ξ|^2, \;ξ\in \mathbb{R}^d\}$ at the Stein-Tomas exponent. Extremizers exist in all dimensions and extremizing sequences are precompact modulo symmetries conditional on a certain inequality, which we verify in the case $d \in \{1,2\}$.

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James Tautges. 2021-12-24. Extremizers for Adjoint Restriction to a Pair of Reflected Paraboloids. https://doi.org/10.1016/j.jfa.2023.110207

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