CORDIS Project
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This project aims to advance the understanding of mathematical conjectures related to the Fourier transform and its restrictions. The focus is on mixed norm analogues and their implications in higher dimensions.
In 1967, Stein proved that the Fourier transform of functions in L^p could be meaningfully restricted to the sphere for certain p>1.
The restriction conjecture, which asserts the maximal range of such p, was solved by Fefferman in two dimensions, but the conjecture remains open in higher dimensions.
Strichartz considered the same question but with the sphere replaced by the paraboloid or the cone, and a great deal of progress has been made in the last two decades by Bourgain, Wolff and Tao, amon…
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