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A calculus of Fourier integral operators with inhomogeneous phase functions on Rd

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Abstract

We construct a calculus for generalized SG Fourier integral operators, extending known results to a broader class of symbols of SG type. In particular, we do not require that the phase functions are homogeneous. An essential ingredient in the proofs is a general criterion for asymptotic expansions within the Weyl-Hörmander calculus. We also prove the L 2(R d)-boundedness of the generalized SG Fourier integral operators having regular phase functions and amplitudes uniformly bounded on R 2d.

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Authors and Affiliations

  1. Dipartimento di Matematica “G. Peano”, Università degli Studi di Torino, Torino, Italy

    Sandro Coriasco

  2. Department of Computer Science, Physics and Mathematics, Linnæus University, Växjö, Sweden

    Joachim Toft

Authors
  1. Sandro Coriasco
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  2. Joachim Toft
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Correspondence to Sandro Coriasco.

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Coriasco, S., Toft, J. A calculus of Fourier integral operators with inhomogeneous phase functions on Rd . Indian J Pure Appl Math 47, 125–166 (2016). https://doi.org/10.1007/s13226-016-0181-8

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  • DOI: https://doi.org/10.1007/s13226-016-0181-8

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