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arXiv · 2605.20100

A discussion of two arguments related to Fefferman's Fourier extension theorem in the plane

Eric T. Sawyer
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Abstract

The Fourier extension conjecture of E. Stein was proved in the plane in 1970 by C. Fefferman, see also Zygmund and Carleson and Sj\"olin, with simplifications given by other authors later on, in particular by L. H\"ormander and T. Tao. We discuss yet two more arguments for this classical theorem on the parabola. The first argument uses C. Fefferman's decoupling together with a decomposition into Haar wavelets. This sets the stage for the second argument whose point of departure is the bilinear characterization of Tao, Vargas and Vega, and relies on the bilinear interplay with the classical wave packet constructions and discrete characterizations.

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Eric T. Sawyer. 2026-05-19. A discussion of two arguments related to Fefferman's Fourier extension theorem in the plane. https://arxiv.org/abs/2605.20100

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