Some remarks on the Mizohata-Takeuchi conjecture

Abstract: This is a conjecture on weighted estimates for the classical Fourier extension operators of harmonic analysis. In particular, let E be the extension operator associated to some surface, and f be a function on that surface. If we 'erase' part of Ef, how well can we control the 2-norm of the remaining piece? The Mizohata-Takeuchi conjecture claims some remarkable control on this quantity, involving the X-ray transform of the part of the support of Ef that we kept. In this talk we will discuss the history of the problem, and will describe a new perspective that modestly improves our knowledge (for a certain class of weights). This is joint work with A. Carbery.

classical analysis and ODEsfunctional analysisrepresentation theoryspectral theory

Audience: researchers in the topic

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