The first result in this paper provides a very general $\epsilon$-removal argument for the multilinear restriction estimate. The second result provides a refinement of the multilinear restriction estimate in the case when some terms have appropriate localization properties; this generalizes a prior result of the author.
The multilinear restriction estimate: a short proof and a refinement
Bounds for Periodic Energy and the Optimality of Two Periodic Point Configurations in the Plane
Bernstein-Nikolskii Inequality: Optimality with Respect to the Smoothness Parameter
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