A probabilistic analogue of the Fourier extension conjecture

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.

100 pages, small corrections to the proof of Lemma 2 on pages 11 and 12, main result unchanged