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arxiv: 1701.03523 · v3 · pith:34E3QO6Fnew · submitted 2017-01-12 · 🧮 math.CA

On the restriction theorem for paraboloid in mathbb R⁴

classification 🧮 math.CA
keywords mathbbestimateparaboloidrestrictionargumentsattentionbarrierbreaking
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We prove that recent breaking by Zahl of the $\frac32$ barrier in Wolff's estimate on the Kakeya maximal operator in $\mathbb R^4$ leads to improving the $\frac{14}{5}$ threshold for the restriction problem for the paraboloid in $\mathbb R^4$. One of the ingredients is a new trilinear estimate. The proofs are deliberately presented in a nontechnical and concise format, so as to make the arguments more readable and focus attention on the key tools.

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