New multiscale polynomial Wolff axioms lead to Kakeya maximal estimates for p ≥ 1 + O(1/n), improving prior bounds in dimensions n=5 and n≥7.
Sharp estimates for oscillatory integral operators via polynomial partitioning
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abstract
The sharp range of $L^p$-estimates for the class of H\"ormander-type oscillatory integral operators is established in all dimensions under a positive-definite assumption on the phase. This is achieved by generalising a recent approach of the first author for studying the Fourier extension operator, which utilises polynomial partitioning arguments.
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math.CA 1years
2019 1verdicts
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Improved bounds for the Kakeya maximal conjecture in higher dimensions
New multiscale polynomial Wolff axioms lead to Kakeya maximal estimates for p ≥ 1 + O(1/n), improving prior bounds in dimensions n=5 and n≥7.