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On the boundedness of certain bilinear oscillatory integral operators


Authors: Salvador Rodríguez-López, David Rule and Wolfgang Staubach
Journal: Trans. Amer. Math. Soc. 367 (2015), 6971-6995
MSC (2010): Primary 35S30, 42B20, 42B99
Published electronically: March 13, 2015
MathSciNet review: 3378820
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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
Email: wulf@math.uu.se

DOI: https://doi.org/10.1090/S0002-9947-2015-06244-8
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
Article copyright: © Copyright 2015 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.