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Improved Fourier restriction estimates in higher dimensions. (English) Zbl 1423.42011

Guth’s approach to the Fourier restriction problem via polynomial partitioning is a basic tool. Improved bounds for the restriction conjecture, particularly in high dimensions, are then obtained by writing out Guth’s induction argument as a recursive algorithm and introducing new geometric information, known as the polynomial Wolff axioms. Consequences for the Kakeya conjecture are also considered.

MSC:

42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
42B20 Singular and oscillatory integrals (Calderón-Zygmund, etc.)
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