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math.CA2026
A discussion of two new proofs of Fefferman's Fourier extension theorem in the plane
Eric T. Sawyer
The Fourier extension conjecture of E. Stein was proved in the plane in 1970 by C. Fefferman, see also Zygmund and Carleson and Sjölin, with simplifications given by other authors…
math.CA2026
A probabilistic analogue of the Fourier extension conjecture
Eric T. Sawyer
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 wit…
math.CA2024
Two weight Sobolev norm inequalities for fractional vector Riesz transforms and doubling weights
Eric T. Sawyer, Brett D. Wick
We prove a T1 theorem for fractional vector Riesz transforms mapping one weighted Sobolev space to another, where the weights are doubling measures on Euclidean space. Boundedness…