On 𝐿^{𝑝} continuity of singular Fourier integral operators

Comech, Andrew; Cuccagna, Scipio

doi:10.1090/S0002-9947-03-02929-5

On $L^{p}$ continuity of singular Fourier integral operators
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by Andrew Comech and Scipio Cuccagna PDF

Trans. Amer. Math. Soc. 355 (2003), 2453-2476 Request permission

Abstract:

We derive $L^{p}$ continuity of Fourier integral operators with one-sided fold singularities. The argument is based on interpolation of (asymptotics of) $L^{2}$ estimates and $\mathrm {H}^1\to L^1$ estimates. We derive the latter estimates elaborating arguments of Seeger, Sogge, and Stein’s 1991 paper. We apply our results to the study of the $L^{p}$ regularity properties of the restrictions of solutions to hyperbolic equations onto timelike hypersurfaces and onto hypersurfaces with characteristic points.

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