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<p>We apply recent circle tangency estimates due to Pramanik–Yang–Zahl to prove sharp weighted Fourier extension estimates for the cone in ℝ<sup>3</sup> and 1-dimensional weights. Theidea of using circle tangency estimates to study Fourier extension of the cone is originally due to Tom Wolff, who used it in part to prove the first decoupling estimates. We make an improvement to the best known Mizohata–Takeuchi-type estimates for the cone in ℝ<sup>3</sup> and the 1-dimensional weights as a corollary of our main theorem, where the previously best known bound follows as a corollary of refined decoupling estimates.</p>

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A sharp weighted Fourier extension estimate for the cone in ℝ3 based on circle tangencies

  • 期刊论文

  • 发表日期：

    2026年4月19日

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  • Alexander Ortiz

摘要

We apply recent circle tangency estimates due to Pramanik–Yang–Zahl to prove sharp weighted Fourier extension estimates for the cone in ℝ3 and 1-dimensional weights. Theidea of using circle tangency estimates to study Fourier extension of the cone is originally due to Tom Wolff, who used it in part to prove the first decoupling estimates. We make an improvement to the best known Mizohata–Takeuchi-type estimates for the cone in ℝ3 and the 1-dimensional weights as a corollary of our main theorem, where the previously best known bound follows as a corollary of refined decoupling estimates.