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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the failure of the factorization condition for non-degenerate Fourier integral operators


Author: Michael Ruzhansky
Journal: Proc. Amer. Math. Soc. 130 (2002), 1371-1376
MSC (1991): Primary 35A20, 35S30, 58G15, 32D20
Published electronically: October 12, 2001
MathSciNet review: 1879959
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Abstract: In this paper we give examples of polynomial phase functions for which the factorization condition of Seeger, Sogge and Stein (Ann. Math. 134 (1991)) fails. The corresponding Fourier integral operators turn out to be still continuous in $L^p$. We also give examples of the failure of the factorization condition for translation invariant operators. In this setting the frequency space must be at least 5-dimensional, which shows that the examples are optimal. We briefly discuss the stationary phase method for the corresponding operators.


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Additional Information

Michael Ruzhansky
Affiliation: Department of Mathematics, Imperial College, 180 Queen’s Gate, London SW7 2BZ, United Kingdom
Email: ruzh@ic.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-01-06210-4
PII: S 0002-9939(01)06210-4
Received by editor(s): June 22, 1999
Received by editor(s) in revised form: October 30, 2000
Published electronically: October 12, 2001
Communicated by: Christopher D. Sogge
Article copyright: © Copyright 2001 American Mathematical Society