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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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On the failure of the factorization condition for non-degenerate Fourier integral operators
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by Michael Ruzhansky
Proc. Amer. Math. Soc. 130 (2002), 1371-1376
DOI: https://doi.org/10.1090/S0002-9939-01-06210-4
Published electronically: October 12, 2001
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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.
References
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Bibliographic Information
  • Michael Ruzhansky
  • Affiliation: Department of Mathematics, Imperial College, 180 Queen’s Gate, London SW7 2BZ, United Kingdom
  • MR Author ID: 611131
  • Email: ruzh@ic.ac.uk
  • 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
  • © Copyright 2001 American Mathematical Society
  • 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
  • MathSciNet review: 1879959