On 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 | References | Similar Articles | Additional Information

Abstract: We derive continuity of Fourier integral operators with one-sided fold singularities. The argument is based on interpolation of (asymptotics of) estimates and 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 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

DOI:
http://dx.doi.org/10.1090/S0002-9947-03-02929-5

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