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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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On the boundedness of certain bilinear oscillatory integral operators
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by Salvador Rodríguez-López, David Rule and Wolfgang Staubach PDF
Trans. Amer. Math. Soc. 367 (2015), 6971-6995 Request permission

Abstract:

We prove the global $L^2 \times L^2 \to L^1$ boundedness of bilinear oscillatory integral operators with amplitudes satisfying a Hörmander-type condition and phases satisfying appropriate growth as well as the strong non-degeneracy conditions. This is an extension of the corresponding result of R. Coifman and Y. Meyer for bilinear pseudodifferential operators, to the case of oscillatory integral operators.
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Additional Information
  • Salvador Rodríguez-López
  • Affiliation: Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden
  • Address at time of publication: Department of Mathematics, Imperial College London, 180 Queen’s Gate, London, SW7 2AZ, United Kingdom
  • Email: salvador@math.uu.se, s.rodriguez-lopez@imperial.ac.uk
  • David Rule
  • Affiliation: Mathematics Institute, Linköping University, 581 83 Linköping, Sweden
  • Email: david.rule@liu.se
  • Wolfgang Staubach
  • Affiliation: Department of Mathematics, Uppsala University, 751 06 Uppsala, Sweden
  • MR Author ID: 675031
  • Email: wulf@math.uu.se
  • Received by editor(s): February 13, 2013
  • Received by editor(s) in revised form: June 18, 2013
  • Published electronically: March 13, 2015
  • Additional Notes: The first author was partially supported by the Grant MTM2010-14946
    The third author was partially supported by a grant from the Crawfoord Foundation
  • © Copyright 2015 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Trans. Amer. Math. Soc. 367 (2015), 6971-6995
  • MSC (2010): Primary 35S30, 42B20, 42B99
  • DOI: https://doi.org/10.1090/S0002-9947-2015-06244-8
  • MathSciNet review: 3378820