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

Authors: Andrew Comech and Scipio Cuccagna
Journal: Trans. Amer. Math. Soc. 355 (2003), 2453-2476
MSC (2000): Primary 35S30
Published electronically: February 7, 2003
MathSciNet review: 1973998
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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 $\matheurm{H}^1\to L^1$ 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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Additional Information

Andrew Comech
Affiliation: Department of Mathematics, University of North Carolina, Chapel Hill, North Carolina 27599

Scipio Cuccagna
Affiliation: Department of Mathematics, University of Virginia, Charlottesville, Virginia 22903

Received by editor(s): September 4, 1998
Received by editor(s) in revised form: June 3, 2001
Published electronically: February 7, 2003
Additional Notes: Both authors were partially supported by grants from the National Science Foundation.
Article copyright: © Copyright 2003 American Mathematical Society

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