Sharp local smoothing estimates for Fourier integral operators
Sharp local smoothing estimates for Fourier integral operators
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Christopher Sogge, Johns Hopkins University
We present joint work with D. Beltran and J. Hickman on sharpÌýlocalÌýsmoothingÌýestimates for general Fourier integral operators.ÌýÌýLocalÌýsmoothingÌýbounds imply major estimates in harmonic analysis, including Bochner-Riesz estimates, oscillatory integral estimates and bounds for the size of Besicovitch sets and related problems involving Kakeya maximal functions.Ìý Our work gives a sharp resolution to the most general form of theÌýlocalÌýsmoothingÌýproblem formulated by the speaker in the early 1990s.Ìý We rely on decoupling estimates of Bourgain and Demeter.