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

DOI:
https://doi.org/10.1090/S0002-9939-01-06210-4

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 . 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:
https://doi.org/10.1090/S0002-9939-01-06210-4

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