Claims a proof of the paraboloid Fourier extension conjecture in d≥3 via smooth Alpert wavelets, grid averaging, and a periodic stationary phase lemma.
A probabilistic analogue of the Fourier extension conjecture
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abstract
We prove a probabilistic Fourier extension theorem that says Fourier extension holds when averaged over certain smooth Alpert multipliers. The proofs use smooth Alpert wavelets with the classical techniques of stationary phase and interpolation of L^2 and L^4 estimates. The correct L^4 bounds for resonant forms require an expectation over Alpert multipliers.
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math.CA 2representative citing papers
Discusses two alternative proofs of Fefferman's Fourier extension theorem using decoupling and wavelet decompositions, with one method extended to higher dimensions.
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A smooth Alpert testing characterization of convolution type for the Fourier extension conjecture on paraboloids
Claims a proof of the paraboloid Fourier extension conjecture in d≥3 via smooth Alpert wavelets, grid averaging, and a periodic stationary phase lemma.
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A discussion of two new proofs of Fefferman's Fourier extension theorem in the plane
Discusses two alternative proofs of Fefferman's Fourier extension theorem using decoupling and wavelet decompositions, with one method extended to higher dimensions.