University of Birmingham > Talks@bham > Analysis Seminar > Local smoothing estimates for Fourier Integral Operators and wave equations

Local smoothing estimates for Fourier Integral Operators and wave equations

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If you have a question about this talk, please contact Diogo Oliveira E Silva.

The sharp fixed-time Sobolev estimates for Fourier Integral Operators (and therefore solutions to wave equations in Euclidean space or compact manifolds) were established by Seeger, Sogge and Stein in the early 90s. Shortly after, Sogge observed that a local average in time leads to a regularity improvement with respect to the sharp fixed-time estimates. Establishing variable-coefficient counterparts of the Bourgain-Demeter decoupling inequalities, we improved the previous known local smoothing estimates for FIOs, and we show, in particular, that our results are sharp in both the Lebesgue and regularity exponent (up to the endpoint) in odd dimensions. This is joint work with Jonathan Hickman and Christopher D. Sogge.

This talk is part of the Analysis Seminar series.

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